Non-linear Dynamics Commons^™

Numerical Methods For Nonlinear Problems Using The Finite Element Method, Logan Price

Discovery Day - Daytona Beach

Numerical Methods for Nonlinear Problems Using the Finite Element Method is a computational mathematics capstone that builds and tests finite element method (FEM) workflows for nonlinear partial differential equations in FreeFEM++, with ParaView used for visualization. Two nonlinear model problems are used to demonstrate the approach. The first is a semilinear reaction-diffusion equation with a cubic nonlinearity. A manufactured solution is used so accuracy can be checked at a fixed final time, and refinement studies in both time step and mesh size are run while nonlinear iteration counts are tracked to show solver effort. The second problem is the steady …

From Homogeneous To Heterogeneous Adaptive Bounded-Confidence Opinion Dynamics On Networks, Sally Hafez, Fatma R. Farag, Amira S. N. Tawadros

Northeast Journal of Complex Systems (NEJCS)

Adaptive bounded-confidence models (ABCMs) elucidate the coevolution of agent states and network structure via local interactions and rewiring mechanisms. Traditional formulations assume uniform interaction parameters, leading to distinct regime shifts encompassing fragmentation, polarization, and consensus. A symmetric heterogeneous extension of the adaptive bounded-confidence model is introduced, in which interaction parameters vary according to whether agents belong to the same or different groups. The model retains the original update and rewiring protocols but integrates within-group and between-group confidence bounds alongside tolerance thresholds. Initially, the classic homogeneous model is replicated to establish a reference point. Subsequently, the heterogeneous extension is assessed under …

Information Theory Analysis Of Water Vapor Stable Isotopes From The Sail Campaign, Matthew John Rybecky

Earth and Planetary Sciences ETDs

Understanding the processes that control water vapor isotopic composition in mountain environ- ments is essential for interpreting isotope records and predicting water resource responses to cli- mate change. This thesis applies information theory to continuous, high-resolution water vapor stable isotope measurements from the Surface Atmosphere Integrated Field Laboratory (SAIL) campaign in the East River watershed of Colorado’s Upper Gunnison Basin, spanning the winter- to-spring transition of 2022–2023. The analysis employs Shannon entropy, mutual information, transfer entropy, and joint transfer en- tropy (JTE) to quantify how environmental variables, including surface meteorology, radiation, tur- bulent fluxes, and ERA5 reanalysis products, transfer information …

Sustainable Consumer Behavior Modeling: A Complex-Systems Approach To Neuromarketing, Preethi Nanjundan, Nupoor Sanjay Bhute, Ragini Topre, Lijo Thomas

Northeast Journal of Complex Systems (NEJCS)

This study examines the application of complex-systems modeling to neuromarketing data for gaining deeper insights into the mechanisms underlying sustainable consumer behavior. It investigates how neural and biometric responses, interpreted through a systems-based perspective, can uncover dynamic interactions, feedback mechanisms, and emergent behavioral patterns influencing sustainable purchase decisions. The research explores the impact of sustainability-oriented marketing stimuli on long-term behavioral intentions by emphasizing the interconnected roles of cognitive processing, emotional engagement, implicit associations, and collective consumer dynamics. Through simulation-based modeling and structural analysis, the study demonstrates how subconscious neural responses and affective mechanisms mediate the relationship between marketing interventions, consumer …

Provocable Forgiveness In Noisy Brand--Consumer Systems:An Agent-Based Study Of Repeated Interaction, Tahere Ahmadiyan, Hamidreza Navidi, Behbod Keshavarzi

Northeast Journal of Complex Systems (NEJCS)

Repeated brand--consumer exchange is often treated as a managerial problem of loyalty, recovery, and trust. It can also be read as a small complex system: many local decisions about cooperation, retaliation, and forgiveness accumulate into market-level selection. This study uses that perspective to examine which relational rules survive when communication is imperfect. Eight canonical Iterated Prisoner's Dilemma strategies are translated into marketing archetypes and evaluated through round-robin tournaments, a six-level noise sweep, proportional-fitness ecological dynamics, and finite-population Moran invasion tests. The tournament leaderboard is calculated without same-strategy self-play, so that reported payoffs reflect inter-archetype competition rather than homogeneous self-coordination. At …

A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis, Paige Zhu, Padmanabhan Seshaiyer

CODEE Journal

Chronic post-surgical pain (CPSP) is a common and often overlooked complication following surgical correction of idiopathic scoliosis, impacting long-term patient wellbeing despite improvements in surgical outcomes. This project introduces a novel epidemiological framework to model the progression of CPSP using a compartmental structure. By applying a coupled system of nonlinear differential equations, we simulate pain trajectories over time and assess the effectiveness of surgical interventions. The model is implemented for a single-cohort population and extended to a two-cohort design to compare outcomes between Posterior Spinal Fusion (PSIF) and Vertebral Body Tethering (VBT) procedures. Further stratification by patient age enables us …

Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender

Mathematics Theses and Dissertations

This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …

Adaptive Intervention Strategies In Co-Evolving Multiplex Networks: A Reinforcement Learning Approach To Real-Time Misinformation Containment, Anjali Ashokrao Bhadre Dr., Harshvardhan Prabhakar Ghongade Dr.

Northeast Journal of Complex Systems (NEJCS)

The growing transmission of misinformation via social media creates serious challenges to public health, democracy and social cohesion. To date, methods used to contain misinformation rely upon static representations of networks and set rules for interventions. In contrast, this study presents the first Multiplex Adaptive Reinforcement Intervention Network (MARIN), a framework for real-time adaptive intervention in the context of dynamic misinformation transmission using co-evolving multiplex networks and deep reinforcement learning. Unlike past studies that have assumed static network structures, MARIN has the ability to allow for dynamic changes in network topology as a result of both misinformation transmission and intervention …

The Dynamics Of Educational Change: A Complex Systems Perspective, Preethi Nanjundan, Lijo Thomas, Abith K. Sunil

Northeast Journal of Complex Systems (NEJCS)

The perception of university teachers toward educational reforms plays an important role in determining the success of changes introduced in the education sector. This study focuses on teachers’ attitudes toward change, their emotional responses, and their overall views on educational reforms. Across the world, many educational reforms have failed to achieve their expected outcomes in improving teaching practices and student learning. As education systems are highly complex, the approach toward implementing reforms has also changed over time. Some reforms are introduced gradually, while others involve major innovations within the system. Complexity theory provides useful insights and tools that help educators …

A Professional Development Course On Data-Driven Dynamical Systems At A Primarily Undergraduate Institution: Part A - Scientific Content, Alessandro M. Selvitella, Jeffrey R. Anderson

CODEE Journal

In the age of data-driven decision making, ordinary differential equations (ODEs) remain a powerful and interpretable framework for modeling dynamic processes, especially when integrated with modern tools from statistical learning and data-driven dynamical systems. Yet, general undergraduate and graduate curricula do not typically address key opportunities in data-driven dynamical systems.

This first paper in a series focuses on the mathematical and methodological core of a professional development course first developed in the academic year 2025-2026 at a Primarily Undergraduate Institution, Purdue University Fort Wayne. The curriculum developed in this course emphasized how regression, regularization, and sparse identification can be used …

Decoding Stock Market Movements: The Role Of Unemployment And Volatility, Bipllab Roy, Suparna Bhattacharjee

Northeast Journal of Complex Systems (NEJCS)

This study investigates how unemployment and market volatility interact with stock prices in the Indian context, framing the stock–labour–volatility nexus as a complex adaptive system (CAS) rather than a set of linear, time-invariant relationships. Using verified secondary data on unemployment, India VIX, and NSE stock indices for 2013–2023, we first apply simple and multiple regression as a descriptive baseline. Results show a strong negative association between unemployment and stock prices (R ≈ 0.824, R² ≈ 0.68, p < 0.05), consistent with Keynesian demand-side channels, while the linear VIX–stock relationship is weak and statistically insignificant (R² ≈ 0.07, p > 0.05), consistent with the expectation that volatility operates through non-linear, regime-dependent mechanisms not captured by OLS.

Importantly, we document and transparently disclose critical …

Developing A Framework For Mooc Dropout: The Role Of Utilitarian And Hedonic Values In Student Retention, Bipllab Roy, Mave D'Souza, Madhura Laghane

Northeast Journal of Complex Systems (NEJCS)

Massive Open Online Courses (MOOCs) have expanded access to higher education but continue to face persistently high dropout rates, raising concerns about their long‑term effectiveness and sustainability. This study develops and empirically tests a structural framework that links utilitarian values (perceived usefulness, certificate value, time flexibility), hedonic values (enjoyment, variety and novelty, personal interest alignment), and individual characteristics (goal orientation, self‑efficacy, motivation type) to MOOC student retention. Data were collected through a structured questionnaire administered to 200 MOOC learners from Christ University, Lavasa Campus, and analyzed using Structural Equation Modelling (SEM) in AMOS. The results show that goal orientation, self‑efficacy …

Distributed Self-Control Of Dynamical Networks By Adaptive Link Weight Adjustments, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

Conventional control theory considers controlling the behavior of a dynamical system toward a desired state by injecting externally designed inputs into the system. Meanwhile, most complex systems exhibit self-organization through local information exchanges among individual dynamical components that are embedded within a complex network of interactions. The self-organizing dynamics of those systems are realized in a highly distributed manner using locally available information only, and therefore, their behaviors have not been discussed much from a control theoretic viewpoint. Meanwhile, adaptive networks, i.e., dynamical networks whose states and topologies coevolve at similar time scales, can offer a promising theoretical framework in …

Exploring Maximal Length Cellular Automata To Generate Primitive Polynomials In Gf(2), Sumit Adak, Subhrajit Deb, Anurag Ghosh, Angshuman Roy, Souvik Roy

Northeast Journal of Complex Systems (NEJCS)

We present a simple method that uses cellular automata (CAs) to find primitive polynomials over GF(2). We used maximal length CAs as tools to generate primitive polynomials. It is usually very difficult to find maximal length CAs or primitive polynomials since they require exponential time, and there is no linear time method. However, in our work, given an n-size specific sequence of CA with reasonable probability, our technique computes a cycle of length at most 2^n-1 (maximal length) in O(n) time. The characteristic polynomials of synthesized maximal length CAs are claimed to be primitive since it was previously established that …

Decision Making At Triage Classification Using Svm With Smote Technique, Mehanas Shahul, Pushpalatha Kp

Northeast Journal of Complex Systems (NEJCS)

The efficient functioning of triage gates in overcrowded emergency departments (EDs) occurs in the context of the complex adaptive system (CAS) framework, where diverse system elements – patients, medical personnel, resources, patients’ inflow patterns, and patients themselves – simultaneously and dynamically influence the decision process. This study addresses the automated incorporation of machine learning triage algorithms as part of the system triage process to support automated classified risk-level recognition based on a limited set of vital signs. Patients are dynamically subsumed under high and low-risk categories enhanced by sensitivity, which enables optimal diagnosis and triage response to the critical clinician …

Uncovering Discrete States From Multimodal Psychophysiological Data Using Gaussian Latent Dirichlet Allocation (Glda), Congyu Wu, Aaron Fisher, David Schnyer

Northeast Journal of Complex Systems (NEJCS)

In this article we explore and validate the utility of an unsupervised probabilistic model, Gaussian Latent Dirichlet Allocation (GLDA), for discovering discrete states from repeated, multimodal psychophysiological samples collected from multiple individuals. Psychology and medical research heavily involves measuring potentially related but individually inconclusive variables from a cohort of participants to derive diagnosis, necessitating clustering analysis for state identification. Traditional probabilistic clustering models such as Gaussian Mixture Model (GMM) assume a global mixture of component distributions, which may not be realistic for observations from different patients. The GLDA model borrows the individual-specific mixture structure from a popular topic model Latent …

Asymmetric Opinion Formation Of Emotional Excitable Agents, Irene Ferri, Emanuele Cozzo, Aleix Nicolás-Olivé, Albert Díaz-Guilera, Luce Prignano

Northeast Journal of Complex Systems (NEJCS)

The bounded confidence model represents a widely adopted framework for modeling opinion dynamics wherein actors have a continuous-valued opinion and interact and approach their positions in the opinion space only if their opinions are within a specified confidence threshold. Here, we propose a novel framework where the confidence bound is determined by a decreasing function of their emotional arousal, an additional independent variable distinct from the opinion value. Additionally, our framework accounts for agents' ability to broadcast messages, with interactions influencing the timing of each other's message emissions. Our findings underscore the significant role of synchronization in shaping consensus formation. …

Accuracy Of Parameter Estimation For A Simple Gene Regulatory Network Model Is Sensitive To Network Motif, Number Of Parameters Estimated, And Magnitude And Direction Of Regulatory Relationships, Nikki C. Chun, Kam Dahlquist

Honors Thesis

A gene regulatory network (GRN) is a set of transcription factors that regulate the expression of genes encoding other transcription factors. The dynamics of a GRN explain how gene expression changes over time. GRNmap is a MATLAB software package that uses ordinary differential equations to model dynamics of small-scale GRNs. We used the program to estimate production rates, expression thresholds, and regulatory weights for each transcription factor in three related literature-derived GRNs based on yeast cold shock microarray data previously collected in the Dahlquist Lab. We noticed large differences in estimated weight values when 1-2% of the expression values were …

Dynamic Homeostasis In Relaxation And Bursting Oscillations, Christopher J. Ryzowicz

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling, Control Analysis, And Parameter Estimation Of Epidemic Dynamics Using The Unscented Kalman Filter, Muhammad Imran, Saira Batool, Brett Mckinney

Biology and Medicine Through Mathematics Conference

No abstract provided.