Non-linear Dynamics Commons^™

Construction And Data-Driven Analysis Of A Stochastic, Individual-Based Opioid Epidemiology Network Model, Leigh Bennett Pearcy, Owen Queen, Vincent Jodoin, Suzanne Lenhart, Christopher Strickland

Mathematical Modelling and Numerical Simulation with Applications

While substance use epidemiology has been an active area of mathematical research in recent years, the social and mental processes that are involved in the development of substance use disorders have presented challenges to advancing the epidemiological theory and how they differ from the contraction of pathogenic disease. Such distinction is especially pertinent in the context of the current United States opioid epidemic and its intersection with the recent COVID-19 pandemic, as both prescription drugs and social influence play major roles in the development of opioid use disorder. In this paper, we construct a stochastic network model capturing how individual …

Optimal Control Of Stochastic Systems: A Numerical Study Of The Stochastic Linear Quadratic Regulator Framework, Gülşen Orucova Büyüköz, Yaprak Güldoğan Dericioğlu, Tuğçem Partal

Mathematical Modelling and Numerical Simulation with Applications

Optimal control of stochastic linear systems is fundamental in control theory, with applications in robotics, finance, and engineering. The Stochastic Linear Quadratic Regulator (SLQR) derives optimal feedback laws via the Riccati equation but requires numerical discretization of the resulting stochastic dynamics. Despite extensive studies on numerical methods for stochastic differential equations, their performance within the SLQR framework remains insufficiently explored. This study compares two predictor–corrector schemes of different orders: the Order 1.0 Predictor-Corrector (PC) method and the Order 2.0 Weak PC method. A one-dimensional linear quadratic problem with a closed-form solution enables precise error evaluation against the analytical trajectory. Convergence …

Mathematical Analysis And Numerical Simulation Of A Fractional-Order Sir-Si Model For Malaria Transmission Dynamics, Gassan A. M. O. Farah, Abdulaziz Y. A. Mukhtar, Kailash C. Patidar

Mathematical Modelling and Numerical Simulation with Applications

This study investigates the complex transmission dynamics of malaria, a critical global health challenge, with a focus on the African continent. We introduce a novel approach that employs Fractional Differential Equations (FDEs) to advance the understanding of malaria spread and control. Specifically, we develop a new SIR-SI model using the Caputo fractional operator, which captures the memory effects and time-delay characteristics inherent in real-world epidemiological systems. A detailed analysis of the model's solvability and uniqueness is conducted using fixed-point theory. To obtain an analytical solution, the system is solved via the Laplace transform method, with solutions expressed in closed form …

A Parallel Interval Modeling Framework For Nonlinear Systems: Application To A Modified Duffing Oscillator, Roman Voliansky, Nina Volianska

Northeast Journal of Complex Systems (NEJCS)

The paper presents a mathematical framework for converting nonlinear dynamical systems into parallel forms. This framework replaces the exact system motion equations with interval equations, enabling the representation of nonlinear functions over piecewise linear domains. Such representation enables the description of system motions using linear-like differential equations, which can be analyzed and manipulated using well-known control methods. One such method is eigenvalue analysis, a powerful tool in classical control theory since many techniques rely on the system’s characteristic polynomial and its eigenvalues. We apply this method to define interval system eigenvalues and track their variation during system operation. These eigenvalues …

Coupled Machine Learning Models: Combining Observations And Numerical Analysis In A Physics-Regularized Approach, Austin B. Schmidt

LSU New Orleans Theses and Dissertations

This dissertation investigates surrogate modeling for fixed-location environmental forecasting using novel data-combination techniques. The work surveys the landscape of observational measurements and numerically generated data, identifying similar research and gaps in current methodologies. The ratio-coupled training framework is introduced to combine two data sources per predicted feature through a tunable parameter that weights training signal strength. An optimization scheme is developed to simultaneously tune surrogate weights and the coupled signal ratio, allowing relative influence between signals to act as an explicit regularizer. Three case studies demonstrate the methodology and approach in a variety of contexts. The first study is based …

Grokking Applied To Chaotic Iterates Of The Logistic Map, Felix Donkoh

Electronic Theses and Dissertations

This thesis investigates grokking, the delayed transition from memorization to generalization in neural networks trained on deterministic chaotic data. Using an integer–arithmetic discretization of the logistic map, yn+1 =( a yn(p − yn))/ p 2 , bounded aperiodic sequences were generated across control parameters α ranging from 3.0 to 4.0. Transformer-based models displayed characteristic grokking curves. In periodic and chaotic regimes, validation accuracy rose suddenly after long plateaus, while at the Feigenbaum boundary (α ≈ 3.57) generalization failed completely. Increasing data diversity restored learning in chaotic domains, and explicit α–conditioning enabled a single network to generalize across all regimes. A …

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Immune Dysregulation In Covid-19: Mathematical Modeling Of The Within-Host Dynamics, Pagnapech Ngoun, Nicolas Alvarez, Ayesh Awad, Hwayeon Ryu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Kadel] Robust Basins, Fragile Attractors: A New View On Boolean Network Dynamics, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Metapopulation Model For Oyster Restoration, Leah Shaw

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Heterogeneity In Malaria: A Pk-Pd Immuno-Epidemiology Model With Non-Exponential Waiting Times, Katharine Gurski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach, Bernard Asamoah Afful, Luis F. Gordillo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Balancing Stability And Complexity In Boolean Models Of Biological Networks, Venkata Sai Narayana Bavisetty

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Consideration Of Two Scalarization Methods For The Multi-Objective Nurse-To-Patient Assignment Problem, Ilgın Acar, Steven E. Butt, Aydın Sipahioğlu, İslam Altın

Mathematical Modelling and Numerical Simulation with Applications

In this research, the application of two scalarization methods, namely the conic scalarization method and the $\varepsilon$-constraint method, is investigated within the context of a multi-objective optimization problem. These methods are used to address the challenge of assigning nurses to patients on a hospital unit during a shift. The two objective functions of this assignment problem are based on patient workload metrics and unit-related travel distance measures. The proposed solution approach demonstrates the ability to generate solutions that eluded the previous mathematical programming techniques that relied on simplistic weightings of conflicting objective functions. In addition, it is found that the …

Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro

Mathematical Modelling and Numerical Simulation with Applications

In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized …

Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk

Mathematical Modelling and Numerical Simulation with Applications

This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_01$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents …

Some New Three-Term Conjugate Gradient Methods For Riemannian Optimization With Application To The Gough-Stewart Platform, Nasiru Salihu, Poom Kumam, Lin Wang, Sani Salisu

Mathematical Modelling and Numerical Simulation with Applications

Three-term conjugate gradient (TTCG) methods have been extensively studied for optimization within Euclidean geometry, with some inherently satisfying the sufficient descent property, thus enhancing their theoretical superiority. However, other TTCG methods have been developed that incorporate restarting the search direction, simplify the steepest descent approach, or rely on the convexity assumptions of f to establish their convergence results. This paper introduces the Riemannian three-term conjugate gradient (RTTCG) methods. The search direction in these RTTCG methods consistently satisfies the sufficient descent condition, regardless of the line search employed, and does so without requiring a restart mechanism. By utilizing retraction and vector …

Potential Pitfalls In Visual Models Of Tipping Points - And How To Fix Them, Jonathan Dechert, Svetlana Gurevich, Stefan Heusler

Northeast Journal of Complex Systems (NEJCS)

Visual models play a crucial role in both science and science communication. However, the distinction between mere analogies and mathematically sound graphical representations is not easy and can be misunderstood not only by laypeople but also within academic literature itself. Moreover, even when the graphical representation exactly corresponds to the mathematical model, its interpretation is often far from obvious. In this paper we discuss the potential landscape visualization commonly used for tipping points in the context of nonlinear dynamics and reveal potential pitfalls, in particular when distinguishing bifurcation induced tipping (B-tipping) from noise-induced tipping (N-tipping).

We propose new visualization techniques …

Topological And Information-Theoretic Analysis Of Climate-Driven Indonesian Throughflow Dynamics, Sandy H. S. Herho, Katarina E.P. Herho, Iwan P. Anwar, Rusmawan Suwarman

Northeast Journal of Complex Systems (NEJCS)

The Indonesian Throughflow (ITF) represents the sole tropical pathway connecting Pacific and Indian Oceans, yet quantitative understanding of climate mode influences on its variability remains incomplete. We applied information-theoretic and topological frameworks to analyze 34 years (1984-2017) of observational ITF transport data alongside ENSO and IOD indices. Bootstrap analysis revealed pronounced ITF seasonality with 13.28 Sv amplitude peaking in September, contrasting with negligible climate index annual cycles, indicating scale separation in forcing mechanisms. Multi-method extrema detection identified 36-41 extreme events per variable, with 23.1% coincidence between ENSO and IOD high extrema confirming known co-occurrence patterns. Ensemble information-theoretic metrics demonstrated ENSO …

Mass Effects On Energy Transfer Paths In Nonlinear Vibrating Systems, Manal Mustafa

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

This dissertation examines the role of mass in nonlinear systems, uncovering its role in enabling passive energy redistribution and robust vibration control in both idealized and real-world structures. Focusing on a strongly nonlinear two-degree-of-freedom system, it investigates how changes in mass ratio influence the dynamics of energy transfer, nonlinear normal modes (NNMs), and dissipation behavior.

A number of significant contributions are introduced in this work beginning with the introduction of the frequency-energy-peaks (FE-pks) plot, a novel tool that visualizes how energy flows through the system, revealing transient resonance orbits, internal resonance effects, and effectively capturing the different nonlinear phenomena with …

Derivation Of Adjoint Based Error Estimates For Nonlinear Ordinary Differential Equations With Application To Multistage Sir Models With Demographics, Daniel Alcala

Mathematics & Statistics ETDs

Ordinary Differential Equations (ODEs) are central to the mathematical modeling of various real-world phenomena, from mechanical systems governed by Newton’s laws to epidemic dynamics described by SIR-type ODEs. Since many ODEs do not admit closed-form analytic solutions, we approximate them numerically (e.g., with Euler’s, Runge–Kutta, or other such methods). This raises the key question: How accurate are these numerical solutions? In particular, reliably estimating the error in some quantity of interest (QoI) at time T without having an exact solution is of great scientific interest.

The first main contribution of this thesis is the development and analysis of adjoint-based error …

Theoretical And Experimental Investigation Of Liquid-Liquid Phase Separation: Characterizing Elastin-Like-Polypeptides, Adam D. Quintana

Chemical and Biological Engineering ETDs

This dissertation develops and validates a semi-empirical Flory–Huggins-based interaction model, combined with Cahn–Hilliard simulations, for predicting multi-component liquid–liquid phase separation (LLPS) in elastin-like polypeptide (ELP) systems. Equilibrium droplet compositions, measured using a PDMS-based microfluidic device, enabled direct parameterization of interaction coefficients. The model was applied to generate phase diagrams and assess composition dependence in ternary mixtures. Cahn–Hilliard simulations were conducted to explore potential phase morphologies under different interfacial conditions. Multi-component Lattice Boltzmann simulations were implemented to model droplet morphology evolution under varying interfacial and diffusive parameters, reproducing experimentally relevant morphologies. A three-phase wetting study revealed conditions for selective wetting and …

Stability Analysis And Extension Of A Discrete-Time Dynamical System For Scaffolded Learning, Kris H. Green, Bernard Ricca

Northeast Journal of Complex Systems (NEJCS)

Van Geert and Steenbeek [16] proposed a coupled, delayed, discrete-time deterministic dynamical system to model scaffolded learning. We provide a detailed analysis of their model, whose global dynamics are complicated by the presence of intersecting lines of non-isolated, nonhyperbolic fixed points. We also interpret some of the trajectories in the system that have interesting dynamics in the context of the teacher-student interactions, and propose an extension to the model that simultaneously collapses the lines of fixed points to single, isolated points and is easily interpreted. These results provide the foundation for guiding the collection and integration of experimental data to …

The Evolution Of Global Gold And Copper Trade Networks, Oleksandr Hulianskyi

Northeast Journal of Complex Systems (NEJCS)

Gold and copper have emerged as two of the most vital commodities in global trade. Despite serving distinct purposes, their international trade networks reveal interconnected patterns, critical to understanding the dynamics of global economics. This paper studies these attributes and their evolution during the last 36 years for both metals and finds correlations between them. The first part of the research is focused on the sustainability of networks through efficiency and robustness indexes; the second part is dedicated to interconnectedness – the Louvain and Bayesian SBM algorithms, partition, and modularity instruments are used. Community detection algorithms provide valuable insights into …

Coarse-Graining Spiking Reservoirs: Reducing Reservoir Size While Preserving Critical Dynamics, Tucker X. Mastin, Christof Teuscher

Northeast Journal of Complex Systems (NEJCS)

We propose an extension of renormalization into the domain of spiking neural networks, thereby providing a novel framework for coarse-graining neural networks without disrupting their critical properties. The proposed coarse-graining technique merges neurons and synaptic connections based on a graph-theoretic distance derived from synaptic weight strength and is configured to effectively prune the reservoir size while preserving the scale-free spiking dynamics indicative of criticality. Criticality in spiking neural networks may provide information-theoretic advantages by optimizing information processing and sensitivity to input. Using time-series prediction benchmarks, we demonstrate that networks operating at criticality exhibit up to 32% higher prediction accuracy before …

Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz

Dartmouth College Ph.D Dissertations

The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals …

Orchestrating Complexity: The Art Of Virtual Leadership In System Modelling, Vijay Kumar Sonawane, Bipllab Roy, Purnendu Bikash Acharjee, Indu Pv

Northeast Journal of Complex Systems (NEJCS)

This paper explores the dynamics of virtual leadership within global remote work environments, focusing on the application of complex system modelling to understand and enhance leadership efficacy. The application of computational modelling has been a regular feature in economics, science and technology fields, however its application in virtual leadership with linkage to sport leadership appears to be a novel concept. Adopting a multidisciplinary approach, this paper incorporates Game Theory as a conceptual framework to make the leadership model more relevant and applicable that can offer simpler understanding of complex play of leadership drivers. The model incorporates five key leadership dimensional …

Leveraging Usage Of Ai In Education: Knowledge, Attitude And Behavioral Analysis On Students, Bipllab Roy, Purnendu Bikash Acharjee, Rohit Kumar Sharma, Ruptaheen Kramsapi, Shruti P

Northeast Journal of Complex Systems (NEJCS)

The paper explores the possible advantages and drawbacks of artificial intelligence (AI) on sustainability, with an emphasis on using AI to positively achieve SDGs. The study finds a significant vacuum in the literature on the association between knowledge, attitudes, and behaviors towards the use of AI tools and techniques in education and demographic characteristics (sex, age, education level, area of study, and city of origin). The purpose of this research is to close this knowledge gap and advance our understanding of how these demographic factors affect the integration of AI in educational environments. The study specifically aims to comprehend how …

Stability Insights From Modeling Chronic Myelogenous Leukemia, Giovani Thai

Master's Theses

This thesis centers around a model for chronic myelogenous leukemia (CML) as it behaves under imatinib treatment, a common medication for CML patients, and the anti-leukemia immune response. The dynamics are represented with a system of nonlinear delay-differential equations first constructed by Kim et al. in 2008, capturing population changes of T-cells and various CML growth stages. We investigate stability in both the clinical and mathematical sense. Through numerical simulations, we computationally incorporate a supplementary treatment plan to determine its effectiveness in aiding immune response and medication in achieving remission and full elimination. The primary goal is to conduct a …

Dual Quaternions For Gravity Recovery Missions, Ryan Kinzie

Doctoral Dissertations and Master's Theses

A dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to Special Euclidean Group 3 through MATLAB simulations. The dual quaternion-based approach shows superior performance over traditional linearized and uncoupled methodologies, in both modeling accuracy of spacecraft translational position, and the ability to control the pose of a test mass relative to its host spacecraft. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a …