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A Nonlinear Map Describing Relaxation to Cluster States in an Adapting Neuronal Network

Published: May 13, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1585-1621, June 2025. Abstract.In this work, we consider clustered activity patterns in coupled networks of model excitatory (E) and inhibitory (I) neurons. In such patterns, neurons form…

Adjoint-Based Projections for Quantifying Statistical Covariance near Stochastically Perturbed Limit Cycles and Tori

Published: May 9, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1455-1493, June 2025. Abstract.This paper presents a new boundary-value problem formulation for quantifying uncertainty induced by the presence of small Brownian noise near normally…

Modeling the Media Impact on the Medication Behavior of Drug-Sensitive Patients in Two-Strain Tuberculosis Transmission and a Case Study

Published: May 9, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1494-1528, June 2025. Abstract.The improper medication behavior among drug-sensitive tuberculosis (TB) patients increases the risk of developing drug resistance, a risk that can be…

Multistability Induced by Higher-Order Self-Dynamics in Kuramoto-Type System and Its Perspective in Voting Dynamics

Published: May 7, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1422-1454, June 2025. Abstract.In this paper, we consider a variant of Kuramoto model with higher-order self-dynamics. With this term, phases can be forced to approach bipolar states,…

A Proof of the Persistence of Anti-integrable States for Three-Dimensional Quadratic Diffeomorphisms

Published: April 28, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1352-1377, June 2025. Abstract.Three-dimensional quadratic diffeomorphisms with quadratic inverse generically have five independent parameters. When some parameters approach infinity, the…

Degeneracy in Negative Feedback (NFBL) and Incoherent Feedforward (IFFL) Loops: Adaptation and Resonance

Published: April 25, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1316-1351, June 2025. Abstract.Degeneracy in dynamic models refers to these situations where multiple combinations of parameter values produce identical patterns for the observable…

Connected McMullen-Like Julia Sets in a Chebyshev–Halley Family

Published: April 23, 2025 07:00

SIAM Journal on Applied Dynamical Systems, Volume 24, Issue 2, Page 1289-1315, June 2025. Abstract.In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev–Halley root-finding algorithms. We show that the dynamics…