Special Session 67: Modeling, Machine Learning and Data Analysis for Complex Systems and Dynamics

Dynamic Modeling and Regulation of Parkinson`s Disease Network

Zilu Cao Chang`an University Peoples Rep of China Co-Author(s):    Zilu Cao, Lin Du, Honghui Zhang, Yuzhi Zhao, Zhuan Shen, Lianghui Qu, Zichen Deng

Abstract: Parkinson's disease (PD) is one of the most common neurodegenerative diseases. Clinical and experimental evidence suggests that, during the progression of PD, neurons within Cortex-basal ganglia-thalamus (CBGT) circuit exhibit the pathological phenomenon such as abnormal beta-band oscillation and excessive synchronization. To understand the influence of electromagnetic induction and the regulatory effect of electromagnetic stimulation in PD, we investigate physiological and pathological states within a CBGT network model. The results show that the magnetic induction plays a dual role: increasing the magnetic coefficient can not only lead physiological firing patterns to transition into pathological intense firing with enhanced beta band power, but also regulate pathological intense firing and transform it back into physiological firing with weak beta-band power. Moreover, external electromagnetic stimulation applied to the globus pallidus externa (GPe) and pyramidal neuron (PY) effectively suppresses intense firing patterns, beta-band power, and abnormal synchronization in STN, indicating a weakening of pathological oscillations. This work not only elucidates the dual regulatory mechanisms of electromagnetic induction on pathological oscillations in PD, but also provides theoretical foundations for developing noninvasive electromagnetic stimulation as a potential therapeutic strategy for PD.

Prescribed performance projective synchronization for unknown complex networks with mismatched dimensions via event-triggered mechanism

Aili Fan Northwestern Polytechnical University Peoples Rep of China Co-Author(s):

Abstract: In this article, we mainly address the function matrix projective synchronization (FMPS) problem with prescribed performance (PP) between a drive network (DN) with time-varying uncertain coupling, and its corresponding response network (RN) with mismatched dimensions. A new hybrid adaptive learning law is proposed, which consists of a discrete adaptive law designed for unknown time-varying coupling coefficients, and a continuous adaptive law designed for time-invariant coefficients. The proposed work extends the adaptive synchronization control that is originally applicable only with the constant coupling coefficient to the case where the coefficients are time-varying. To ensure the state trajectories of the RN are projectively synchronized to those of the DN while complying with PP constraints, a PP controller is designed. Meanwhile, to reduce the communication load, the event-triggered communication (ETC) mechanism is implemented. Finally, the effectiveness of the designed.

Time scale governs explosive transitions in two-layer multiplex networks

Shutong Liu Shaanxi Normal University Peoples Rep of China Co-Author(s):    Shutong Liu, Yuchen Miao, Yi Song, Nannan Zhao, Zhongkui Sun

Abstract: This study investigates the mechanism of explosive oscillation quenching in a two-layer network where oscillators interact with an environmental layer via feedback coupling, with particular focus on how dynamic time scale governs transitions between bistable regimes. It is demonstrated that significant time scale differences induce and enhance explosive nontrivial amplitude death, characterized by prominent hysteresis and emergent bistability between complete synchronization and nontrivial amplitude death. As the time scale parameter varies, the system evolves through multiple dynamical regimes, including semi hysteresis region where amplitude death and nontrivial amplitude death coexist. Furthermore, the work establishes that both the hysteresis associated with explosive death and subsequent multistability regions can be systematically controlled by adjusting the time scale parameter. Moreover, the analysis reveals that strong inter-layer coupling facilitates multistability, while the damping coefficient and intrinsic frequency collectively regulate the accessibility of explosive versus continuous transitions. Theoretical stability boundaries derived through lyapunov analysis show excellent agreement with numerical simulations, validating the proposed mechanisms. This work elucidates the fundamental principles governing explosive oscillations and multistability in multilayer networks, thus providing a new understanding of oscillation control mechanisms, which proves essential for manipulating dynamical behaviors through time scale tuning.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations

Nicolae Tarfulea Purdue University Northwest USA Co-Author(s):

Abstract: In this talk, we introduce a general technique for discovering functional relationships among the components of solutions to initial value problems for systems of differential equations. The approach leverages sparse identification techniques applied to data generated from numerical solutions of the given initial value problem. The central assumption is that only a small number of terms govern the interactions among components, leading to mathematical relations that are sparse within the broader space of possible functions. We demonstrate the effectiveness and versatility of the method through a series of illustrative applications.

On a Splitting Method for Solving of the Nonlinear Schrodinger Equation and Its Generalization to the Manakov System

Michail Todorov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia Bulgaria Co-Author(s):    Meglena Lazarova

Abstract: In this paper we aim to demonstrate that the splitting by physical factors is applicable and can be efficient for solving of the nonlinear Schrodinger equation. Both the linear and nonlinear parts are treated by the Runge-Kutta method, the nonlinear term, however, is linearised by the so-called inner iteration. The method can be expanded and relatively easily applied for 2+1d Schroedinger equation by adding a coordinate splitting of the spatial coordinates as well as to the Manakov system. Then the procedure should be applied for each equation in the system. The conducted numerical simulations and their results are reliable and give good predictions for the material quantities and dynamics of the light. They give very good comparison with the previous papers of the authors got in another methods.

Improving The PERT Activity Duration Estimation

Xiaohui Wang University of Texas Rio Grande Valley USA Co-Author(s):    Gifty Duah and Xiaohui Wang

Abstract: Accurate estimation of activity durations is fundamental in project scheduling, industrial planning, and service systems where uncertainty and variability affect decision-making. Traditional Program Evaluation and Review Technique (PERT) models rely on three subjective time estimates - optimistic, most likely, and pessimistic - to approximate expected activity duration. However, empirical activity durations are frequently skewed, limiting the accuracy of the classical PERT formulation. Existing literature studied approaches utilizing normal or lognormal approximations that worked for data with either symmetric or the right skewed underlying activity distributions, but their applications are limited for moderate or heavily left skewed data. Abdel-Raheem et al. (2018) introduced refinements with triangular distributions due to its comprehensibility to the project planner and proposed a framework allowing the determination of the contract time using deterministic and probabilistic scheduling techniques. This approach has its own limitations. To overcome these limitations and enable broader applications, this study proposes an enhanced method for activity duration estimation using maximum likelihood estimation applied to lognormal distributions. Using empirical production-rate data, we evaluate estimation accuracy and demonstrate improvements over existing methods.

Computational Analysis of Stress-Induced Glucocorticoid Effects on Cognitive Processing

Pengcheng Xiao Kennesaw State University USA Co-Author(s):

Abstract: The focus of this study is to investigate the effects of different stress levels on cognitive outcomes. Emerging evidence has shown that stress-induced release of glucocorticoids acts on glutamate neurotransmission and consequently influences the functionality of cognitive processing. By incorporating the Hypothalamic-pituitary-adrenal (HPA) axis and neuron models, we study the plasticity regulation outcomes based on two types of stress: stress with regular object and stress object with PTSD. The results can help to understand the dynamical mechanism between the glucocorticoids releasing and the neuron plasticity changes due to different stress levels.

Intelligent Modulation of Brain Disorders Driven by Data and Models

HONGHUI ZHANG Northwestern Polytechnical University Peoples Rep of China Co-Author(s):    youyou Si, Hengxi Zhang, Ruimin Dan

Abstract: Based on the whole-brain structural and functional networks, and driven by the dual impetus of models and electroencephalographic data, we design a brain-inspired neural network algorithm and propose targeted theoretical intervention schemes for the detection, prediction, diagnostic analysis and neuromodulatory therapy of brain disorders such as epilepsy, Parkinson's disease and autism, respectively. We also develop cross-patient optimized algorithms and schemes to improve accuracy, reduce energy consumption and enhance generalization ability.

Unraveling Epileptic Dynamics via Neurovascular Coupling: A Tripartite Neuro-Astrocytic-Arteriolar Computational Framework

Liyuan Zhang Beijing University of Technology Peoples Rep of China Co-Author(s):    Liyuan Zhang, Mingai Li,Youjun Liu

Abstract: Epilepsy is a common neurological disorder associated with dysfunction in neurovascular coupling (NVC). To advance beyond current limited models, this study develops a mathematical model integrating neurons, astrocytes, and arterioles to investigate epileptic mechanisms. Neuronal dynamics are described by an extended Hodgkin Huxley model, while arteriole diameter changes are simulated via a filament sliding mechanism in smooth muscle. The model incorporates key ion channels (calcium activated potassium channel, inwardly rectifying potassium channel) and signaling molecules (oxygen, calcium, nitric oxide) to simulate neuro-hemodynamic responses. Results show six transitional neuronal firing patterns under external stimulation, with bifurcation analyses explaining low voltage fast oscillations, tonic spiking, and bursting. Simulations confirm that neuronal activation triggers astrocytic calcium waves, leading to vasodilator release and arteriole dilation. Additionally, asymptotic ionic concentration changes during ischemia, hypoxia, and astrocytic dysfunction are characterized. This multi-pathway NVC framework offers a more realistic and comprehensive perspective on epileptic pathology.