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Nonlinear dynamical systems represent a fundamental area of study in applied mathematics due to their relevance across various disciplines, including physics, biology, and engineering. Their inherent complexity, characterized by phenomena such as bifurcation, chaos, and sensitivity to parameter variations, often limits the effectiveness of traditional manual analysis, particularly when addressing high-dimensional or computationally intensive models. This study aims to address these challenges by applying computational modeling and numerical simulation techniques to analyze the stability of nonlinear dynamical systems. The research employs analytical methods, including equilibrium point identification and linearization, which are then validated and extended through the fourth-order Runge-Kutta numerical method. Simulations were conducted to visualize equilibrium points, phase portraits, and parameter-driven bifurcation phenomena. The findings demonstrate a strong correspondence between analytical and numerical approaches, with minimal error margins (≤1%) observed in equilibrium point estimation, thus confirming the reliability of computational methods. Moreover, the bifurcation analysis revealed critical transitions such as pitchfork and Hopf bifurcations, which indicate sudden shifts from stability to instability behaviors that are difficult to capture through manual calculations alone. The integration of computational approaches provides clear advantages, offering systematic exploration of parameter spaces and detailed visualizations of system dynamics, thereby expanding the scope of stability analysis. In conclusion, this study emphasizes that computational modeling is not only an effective complement to analytical methods but also a necessary strategy for advancing the understanding of nonlinear dynamical systems in applied mathematics.  

The development of electric propulsion systems has become a major focus in efforts to provide energy-efficient and environmentally friendly air propulsion technology. One emerging innovation is the electric motor-based turbojet fan, which is expected to replace conventional fossil-fueled systems. As the need for energy efficiency increases, studies on electrical power consumption and airflow performance are crucial in supporting the development of new-generation propulsion systems. This study aims to evaluate the relationship between nozzle angle and the characteristics of electrical power consumption and airflow velocity in a double-spool turbojet fan. The method used is an experimental test with an ESP32-based control system. The duty cycle is set at 80% to maintain operational stability. Research data is obtained through measurements of electrical current, voltage, and airflow velocity. The nozzle angle variations tested include 13°, 19°, and 25°. The test results show a significant difference between nozzle angle variations on electrical power consumption and wind speed performance. The 13° nozzle angle produces the highest electrical power consumption, indicating a greater energy requirement to maintain airflow. Conversely, the optimal wind speed was found at an angle of 19°, indicating a balance between energy efficiency and aerodynamic performance. Meanwhile, an angle of 25° showed a decrease in performance in terms of both power and speed, making it less effective. In conclusion, the nozzle configuration has a direct influence on energy consumption and fluid dynamics in electric turbojet fan systems. This research provides an important contribution to the design of electric-based propulsion systems by emphasizing efficiency and performance aspects, while supporting the transition to environmentally friendly technologies.

The rise of authoritarian leadership in higher education institutions has become a pressing global issue, affecting academic freedom, institutional autonomy, and the wellbeing of faculty and students. This phenomenon, observed not only in traditionally authoritarian countries but also in democratic contexts, manifests through centralized power, top-down decision-making, and suppression of critical voices. Despite its growing prevalence, empirical research on authoritarian leadership in academia remains limited, with significant gaps in understanding its contextual dynamics, direct impacts on academic communities, and cross-cultural variations. Recent studies have introduced novel theoretical frameworks tailored to academic settings and employed innovative mixed-method approaches to explore mediating factors such as emotional exhaustion and moderating personality traits. These advances have highlighted the complex and contextual nature of authoritarian leadership’s effects, which generally undermine innovation, morale, and performance, although it may increase compliance in specific situations. The negative consequences of authoritarian leadership are evident in reduced creativity and critical thinking, which are fundamental to the academic mission. Faculty members and students may experience heightened stress, diminished job satisfaction, and a decline in engagement. However, some studies suggest that in certain environments, authoritarian leadership can impose order and enhance efficiency in situations requiring immediate decisions. This paper underscores the urgent need for further research and practical interventions to promote adaptive, collaborative, and wellbeing-oriented leadership models in higher education. Such leadership approaches are essential to foster institutional resilience, democratic governance, and inclusive educational practices in an era of global uncertainty and disruption. By shifting towards more participatory leadership styles, higher education institutions can better address the evolving needs of faculty and students, ensuring a thriving academic environment that supports innovation, diversity of thought, and overall wellbeing.

This study aims to analyze the influence of financial performance on firm value in the manufacturing sector listed on the Indonesia Stock Exchange. Financial performance in this study is measured through four main indicators: Return on Equity (ROE), Return on Assets (ROA), Net Interest Margin (NIM), and Debt to Equity Ratio (DER). Meanwhile, firm value is determined using market-based financial ratios. The research method used is a quantitative approach with multiple linear regression analysis. The research data were obtained from publicly available financial reports of manufacturing companies with a total of 84 observations during the study period. This research model was designed to test the extent of influence of each financial performance indicator on variations in firm value. The analysis results show that ROE, ROA, NIM, and DER simultaneously have a significant effect on firm value. Partially, ROE and NIM are proven to have a significant positive impact, meaning that the higher the two ratios, the higher the firm value. Conversely, ROA and DER show a significant negative effect, indicating that an increase in these two variables actually decreases the firm value. These findings indicate different dynamics between financial indicators in influencing market perception. The coefficient of determination (R²) of 30.6% confirms that the variation in firm value can be explained by the four independent variables in the model, while the remainder is influenced by other external factors not included in the study. Therefore, the results of this study provide important insights for management and investors regarding the role of financial indicators in shaping firm value. Management can use these findings to evaluate financial strategies, while investors can use this information to strengthen the basis for investment decisions.

Financial markets are a crucial component of the global economy, where market volatility is a primary concern for investors. This study aims to analyze the relationship between investor behavior and market volatility, focusing on how sentiment and trading behavior influence stock price dynamics. Understanding this relationship can offer valuable insights for investors and policymakers in managing market fluctuations. The study used primary data from questionnaires distributed to 400 investors. The results indicate that risk perception, investment decisions, and investor experience have a positive and significant effect on the perception of market volatility. In contrast, investor emotions, such as fear and anxiety, negatively affect their perception of volatility. The level of uncertainty investors experience significantly influences their assessment of market fluctuations. A higher perceived risk leads to a stronger tendency to perceive increased market volatility. Furthermore, the actions of investors in the stock market impact their perceptions of price changes. More active investors tend to be more aware and sensitive to market fluctuations, while those influenced by negative emotions may underestimate the extent of market changes, leading to a lower perceived volatility. Investors often ignore important market signals when trying to avoid losses, which can impact their investment decisions. Experienced investors, having encountered various market cycles, are better at handling market fluctuations. Their ability to analyze and interpret market information allows them to manage risks more effectively and optimize long-term investment returns.

This study investigates the effect of role stress and job resources on emotional exhaustion, with work-family conflict as a mediating variable among higher education personnel. Employing a quantitative research design with a causality analysis approach, data were collected through a structured questionnaire using a five-point Likert scale. The sample consisted of 200 educational staff at XYZ institution in Bogor Regency, including civil servants, permanent employees, and contract workers. Data analysis was conducted using the Structural Equation Modeling-Partial Least Squares (SEM-PLS) technique with SmartPLS 3 software. The findings revealed that role stress has a positive and significant impact on emotional exhaustion, indicating that increased stress from role demands contributes to higher levels of emotional fatigue. Conversely, job resources were found to have no significant direct effect on emotional exhaustion. Furthermore, work-family conflict significantly mediated the relationship between role stress and emotional exhaustion, suggesting that stress from conflicting work and family demands intensifies emotional exhaustion. However, work-family conflict did not mediate the relationship between job resources and emotional exhaustion. These results emphasize the critical need for effective stress management strategies and support systems that can help reduce work-family conflict to maintain the emotional well-being of education personnel. This study contributes to understanding the psychological dynamics in the workplace and provides insight into improving employee resilience and productivity in educational institutions.

The current development of digital technology has led to the emergence of new literary forms, one of which is cyber literature, utilizing the internet as a medium for the production and distribution of literary works. This phenomenon creates new dynamics in the literary world in terms of form, content, and interaction between readers and writers. This study aims to analyze the forms, characteristics, and implications of cyber literature as a literary expression that has developed in digital spaces. The method used in this analysis is descriptive qualitative with a literature review approach. Data were obtained through observations of cyber literary works found on various digital platforms, as well as through a review of relevant literature. The analysis results show that cyber literature has distinctive characteristics, such as interactivity, the use of multimedia, and openness to reader participation. In addition, the cyber poem "Api Drupadi" by Retno Darsi Iswandari includes hypertext and hyperlinks that connect the poem to other literary works and external websites. The conclusion of this analysis indicates that cyber literature is a form of literary evolution that not only adapts to technological advancement but also expands the traditional boundaries of literature through innovation and new media.

The development of digital technology has changed many aspects of people's lives, including in terms of social justice. On the one hand, digitalization opens up access to information and accelerates global connectivity. However, on the other hand, various serious challenges have emerged in law enforcement. Inequality in access to technology, algorithmic bias, and the rise of cybercrime are the main issues that test the resilience of the current legal system. This paper aims to explore how the law can play an effective and responsive role in maintaining social justice in the digital era. With a qualitative approach based on literature studies, this article presents an analysis of various current academic literature discussing law, social justice, and technology. The results show that the legal system must be able to adapt quickly, not only at the regulatory level, but also in institutional structures and community participation. The role of society is key to building inclusive and sustainable digital justice. Therefore, law in the digital era is not enough to be just a set of rules, but must be a tool for social empowerment that is able to respond to the dynamics of the times without abandoning the values ​​of justice. Collaboration between stakeholders and strengthening digital literacy are important elements in creating a digital space that is fair for all.

This study aims to examine the application of situational leadership theory by the principal of SMP Negeri 2 Sampanahan, Kotabaru Regency, and its impact on organizational behavior within the school environment. A qualitative approach with a case study method was employed, involving in-depth interviews with the principal, teachers, and students. The main focus of the research is to understand how the principal adapts leadership styles according to the needs and conditions of the individuals being led. The findings reveal that the principal successfully applied various leadership styles—ranging from directive, supportive, participative, to delegative—flexibly based on the specific situations encountered. This adaptability positively influenced the organizational climate, fostered harmonious working relationships, and enhanced the motivation and active participation of both teachers and students. The school environment became more conducive and collaborative, ultimately leading to overall performance improvement. These findings highlight the importance of adaptive leadership in education to support the achievement of organizational goals and the development of human resources within schools. This study contributes to the development of leadership practices in educational settings, particularly in the context of educational management that is responsive to both internal and external institutional dynamics.

Ibn Khaldun is recognized as a prominent Muslim thinker who made significant contributions to the fields of economics, sociology, and politics. In his seminal work Muqaddimah, he introduced economic ideas that were far ahead of his time, including the concepts of national wealth, wage theory, market mechanisms, and the role of the state in fiscal policy. This study aims to examine the core economic thoughts of Ibn Khaldun and their relevance to current economic dynamics. Using a qualitative descriptive approach based on literature review, the study finds that many of Khaldun's ideas remain highly relevant, particularly regarding the importance of productivity, fiscal justice, and the integration of social and economic aspects in building a sustainable system. Most people know that Ibn Khaldun is one of the most famous Muslim thinkers, and he did a lot in the fields of politics, economics, and sociology.  In his monumental work, Muqaddimah discusses various long-established economic concepts, such as the market mechanism, wage theory, national wealth, and the role of the state in fiscal policy.  The purpose of this research is to study Ibn Khaldun's ideas on economics and evaluate how these impact contemporary economic developments.  The study found that many of Khaldun's ideas are still relevant today thanks to the use of descriptive qualitative methodology based on literature study. A sustainable and inclusive economic system relies on the idea of productivity as the source of economic growth, fiscal justice in the taxation system, and integration between social and economic aspects.  The results show that classical economic thought not only has historical value, but also offers solutions to many modern economic problems such as inequality, productivity stagnation, and institutional crisis.

Pastoral ministry is a divine calling that demands faithfulness, vigilance, and wholehearted love in caring for God’s flock. However, in the reality of ministry, many church shepherds face complex and burdensome challenges in fulfilling this responsibility. A failure to understand and implement authority based on the character of Christ often becomes the root problem in pastoral ministry. This study aims to explore the dynamics of pastoral ministry in the context of today’s church, particularly in light of 1 Peter 5:1–4. The approach used is qualitative descriptive, based on a literature review, with a focus on relevant theological and pastoral works. The findings reveal that many pastors experience spiritual and emotional exhaustion, especially when their ministry lacks support from an adequate organizational structure, or when the congregation’s expectations are misaligned with the church’s mission. In this context, true shepherding—as explained by figures such as Bill Lawrence and Phil Pringle—must be rooted in Christ as the Head of the Church. A pastor is called to serve with humility, not to dominate or pursue personal interests. Furthermore, a deep understanding of the biblical metaphor concerning the relationship between shepherd and sheep is essential to avoid distortions in meaning and deviant ministry practices. An emphasis on love, responsibility, and exemplary conduct becomes the foundational framework for building an integrous pastoral ministry. This study concludes that pastoral ministry will be more effective when supported by clear church organizational policies, a deep theological foundation, and pure ministry motivations. Thus, pastoral ministry is not merely an administrative task, but a manifestation of God's love expressed through the lives of His servants.

This study aims to analyze the ibdal rule in Arabic word derivation with an integrative approach between traditional methods and modern linguistics. The ibdal rule, namely the change of one letter into another letter in a word, has long been a concern in classical Arabic studies. The traditional approach views ibdal as part of an effort to maintain the purity and beauty of the Arabic language, based on oral history, analysis of ancient poetry, and readings of the Qur'an. Meanwhile, modern linguistics views ibdal as a rational phonological phenomenon, occurring due to phonetic considerations, ease of articulation, and social dynamics. Through an integrative study, this study found that a comprehensive understanding of ibdal can only be achieved by combining an appreciation of classical Arabic heritage with scientific analysis based on modern phonology and morphology. The results of this study indicate that ibdal is not only linguistic, but also reflects the vitality of the Arabic language in responding to changes in the times. The integration of these two approaches also has an impact on the development of curriculum, teaching methods, and the expansion of Arabic language research space towards a more interdisciplinary direction. This study emphasizes the importance of building a scientific attitude that respects tradition while being open to renewal in Arabic studies. Thus, it is hoped that this research can be a significant contribution to the development of Arabic linguistic studies in a contemporary academic context.

This study discusses the evaluation of stakeholder development strategies in strengthening Islamic educational institutions. The study was conducted qualitatively with case studies in several Islamic educational institutions. The active involvement of stakeholders, such as principals, teachers, parents, government, and the community, has proven to be very influential in strengthening educational institutions. Collaborative and participatory strategies between institutions, the community, and the government are able to improve the quality of governance and the competitiveness of Islamic educational institutions. Determining potential stakeholders is a crucial process so that the main needs and expectations can be met optimally. Implementation of modern management, consensus, and routine monitoring and evaluation are the keys to the success of the institutional strengthening strategy. The main obstacle found is the lack of synergy and communication between stakeholders, so that discussion forums and routine training are needed. Transparency and accountability in the management of institutions are also important factors in building stakeholder trust. Continuous evaluation is needed to adjust the strategy to the dynamics of the needs of institutions and the community.    

The film Ngeri-Ngeri Sedap portrays Batak family life with an authentic and emotional approach. This study aims to analyze the authoritarian parenting style implemented by Pak Domu, the head of the family in the film. The research employs a qualitative method with content analysis. Data were collected through observation, documentation, interviews, and literature review. The analysis uses John Fiske’s semiotic approach, which includes three levels: reality, representation, and ideology. The findings reveal that the authoritarian parenting style is reflected through expressions, vocal intonation, behavior, dialogue, character, and conflict throughout the narrative. This parenting style is influenced by conservative, individualistic, fascist, and patriarchal ideologies embedded in the family’s cultural structure. The study highlights that healthy family relationships require honest communication, understanding each member’s feelings and desires, and avoiding coercion in interpersonal interactions. The film’s representation provides broader insight into the impact of authoritarian parenting on family dynamics. Moreover, the film serves as a reflective medium for viewers to recognize the importance of transforming parenting patterns in order to create harmonious family relationships. Therefore, this research contributes to enriching studies on parenting and family relationships within a local cultural context through cinematic representation.

This study examines the social and cultural values in the drama script Gerbong by Agam Wispi through a literary anthropology approach. The research is grounded in the role of literature as a reflection of socio-cultural values, with Gerbong selected for its rich portrayal of post-revolution Indonesian societal dynamics, which has yet to be holistically analyzed from an anthropological perspective. The aim is to identify the manifestations of socio-cultural values through dramatic structures such as dialogue, characterization, and conflict. A qualitative descriptive method was employed, analyzing narrative and symbolic elements within the script. Findings reveal that social values are reflected in non-familial solidarity, critiques of revolutionary injustice, humanism amid adversity, and women’s resistance to stigmatization. Cultural values emerge through the gerbong (train carriage) as a metaphor for resilience, collective sacrifice, and a belief in independence preserved through oral traditions. Intergenerational conflicts between colonial and post-independence values highlight cultural dynamics in postcolonial transition. The study recommends integrating the script into educational curricula, exploring its performative dimensions, and conducting further interdisciplinary research on power relations and gender representation.

Social skills are one of the important aspects for students' social life, especially in building healthy interpersonal relationships, and adapting to their school environment. However, some students experience difficulties in socializing both with peers and their school environment, which will have an impact on the lack of confidence in students and face social anxiety. Research was conducted to identify the effectiveness of group counseling in improving students' social skills. This research uses a literature review method using journals from the last 5 years. The result of this study is that group counseling is an effective intervention in improving students' social skills.    

Improving the quality of education is a strategic challenge for every educational unit, including private elementary madrasahs that carry the Integrated Islamic approach. MIS IT Nurul Ikhwan Cahaya Ananda Palembang as a basic educational institution based on Islamic values ​​and technology, faces various dynamics in managing quality management, ranging from limited resources to the complexity of implementing an internal quality assurance system. This study aims to describe in depth the management strategies applied in improving the quality of education, as well as identifying the challenges and solutions faced by madrasahs in the implementation process. The research method used is descriptive qualitative with data collection techniques in the form of observation, documentation, and in-depth interviews with key informants. The results of the study indicate that madrasahs have implemented quality management through strategic planning, strengthening teacher capacity, integrating technology in learning, and community involvement. Despite challenges such as budget limitations and imbalances in HR competencies, madrasahs are able to present solutions based on collaboration and innovation that are oriented towards the sustainability of education quality.

This study aims to analyze the influence of ethnic relations on the political orientation of the community in Simpang Selayang Village, Medan City. The research method used is descriptive qualitative with data collection techniques through interviews and documentation. The data analysis techniques applied include data reduction, data presentation, and data verification according to Miles and Huberman. This study focuses on two main problem formulations, namely the influence of ethnic relations on political issues and the influence of ethnic relations on political orientation. The results of the study indicate that ethnic identity plays an important role in determining individual political preferences. Ethnic identity serves as a frame of reference that guides political behavior, including in general elections and other political participation. Solidarity between ethnic groups often strengthens political support for candidates who have the same ethnic affiliation, creating a voting pattern that is strongly influenced by ethnic factors. The research findings also reveal that political issues that are relevant to the local community are influenced by the social and cultural context of each tribe. political programs that emphasize local economic development and preservation of tribal culture tend to get greater support. This suggests that understanding the socio-cultural context of ethnic groups is key to formulating effective and inclusive political policies. This study provides new insights into the dynamics of politics in a multi-ethnic society and emphasizes the importance of inclusive policies that take into account ethnic diversity to promote social harmony and political stability in Simpang Selayang Village.

This article discusses citizenship status in Islamic law, focusing on case studies of Muslim minorities in non-Islamic countries, while considering the dynamics of national law and human rights. The research highlights that in Islamic law, citizenship is often associated with membership in the ummah, although modern Muslim states have adopted contemporary citizenship systems. Developments in Indonesian citizenship policies in the last five years, particularly concerning migration and the rights of foreign nationals married to Indonesian citizens, are also analyzed. However, the implementation of these policies faces challenges due to inconsistencies between national law and Islamic principles related to religious identity. The perspective of Islamic law emphasizes the safeguarding essential rights and human worth, in addition to fairness in the treatment of all individuals. The integration of muslim communities residing in western nations poses challenges in distinguishing the majority from extremist minorities. Additionally, equality, the liberty to make individual choices, and partnership are seen as key elements in shaping the societal lives of muslims across western regions. Therefore, a comprehensive understanding of the interaction between national laws and Islamic principles is needed to guarantee the safeguarding of the rights of muslim minorities worldwide.

This study aims to assess the extent to which the influence of the empathic communication approach in counseling guidance has an effect on increasing students' self-confidence at the Daarul Uluum Lido Modern Islamic Boarding School. Empathic communication-based counseling guidance services increase students' interpersonal communication skills by 23%. This approach emphasizes the importance of group dynamics as a medium that helps students feel supported by their peers and becomes a foundation for strengthening their self-confidence. This study uses a quantitative approach with a descriptive method to provide an accurate description of the relationship between the empathic communication approach in counseling guidance and student self-improvement at the Daarul Uluum Lido Islamic Boarding School. The results of the study show that empathic communication has a very significant role in building positive relationships between counselors and students. In addition, this study also found that the role of counselors in implementing empathic communication is still not fully optimal, especially in providing deeper emotional validation to students. Some students feel the need to be heard, they still need stronger encouragement to be more confident in expressing their opinions. Therefore, although this approach has proven effective in increasing students' self-confidence, it still needs to be strengthened in certain aspects so that its impact is more optimal.