Nonlinear Dynamics and Stochastic Modeling of Complex Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 571

Special Issue Editors


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Guest Editor
Institut Jean le Rond d’Alembert, Sorbonne Université, CNRS, UMR 7190, 4 Place Jussieu, CEDEX 05, 75252 Paris, France
Interests: stochastic processes; random walks; fractional calculus; generalizations

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Guest Editor
Departamento de Física, Universidad Nacional de Colombia, Bogota, Colombia
Interests: nonlinear dynamics; statistical mechanics; complex networks; Markov chains; complex systems

Special Issue Information

Dear Colleagues,

In a wide range of phenomena in nature, complexity emerges through an interplay between nonlinearly interacting agents and stochastic effects. Examples include spreading phenomena such as the propagation of epidemics, forest fires, air pollution, chemical reactions, the foraging of animals, and anomalous transport processes in complex networks.

The aim of this Special Issue is to gather contributions from across the disciplines combining methods from nonlinear science with stochastic modeling including random walk approaches.

Subjects include but are not limited to stochastic resetting, population dynamics, epidemic spreading, compartment models, predator-prey models, nonlinear systems with random delay effects and memory, and stochastic chaos.

Dr. Thomas M Michelitsch
Dr. Alejandro Pérez Riascos
Guest Editors

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Keywords

  • stochastic resetting
  • population dynamics
  • epidemic spreading
  • compartment models
  • predator-prey models
  • nonlinear systems with random delay effects and memory
  • stochastic chaos

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Published Papers (1 paper)

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Research

17 pages, 2136 KiB  
Article
Analysis of Variability of Complex Stochastic Oscillations in a Tristable Calcium Model
by Irina Bashkirtseva and Lev Ryashko
Mathematics 2025, 13(7), 1060; https://doi.org/10.3390/math13071060 - 25 Mar 2025
Viewed by 214
Abstract
Motivated by important biophysical applications, we study the stochastic version of a mathematical model of calcium oscillations. For the deterministic model proposed by Li and Rinzel, a parametric zone of tristability, where two stable equilibria and a limit cycle coexist, is found for [...] Read more.
Motivated by important biophysical applications, we study the stochastic version of a mathematical model of calcium oscillations. For the deterministic model proposed by Li and Rinzel, a parametric zone of tristability, where two stable equilibria and a limit cycle coexist, is found for the first time. In this zone, and also in adjacent bi- and monostability zones, different scenarios of noise-induced generation and suppression of complex calcium oscillations are studied in detail. In these studies, along with the traditional direct numerical simulation and statistical processing, a new analytical apparatus of the stochastic sensitivity technique and confidence domains is effectively used. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Stochastic Modeling of Complex Systems)
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