Work

Linear multiplicative noise destroys a two-dimensional attractive compact manifold of three-dimensional Kolmogorov systems

Year: 2025

Type: article

Abstract: In this paper, we first provide the necessary and sufficient algebraic conditions for the three-dimensional Kolmogorov systems possessing a two-dimensional invariant sphere in [Formula: see text]. Then, we establish a global attracting criterion for this invariant sphere in [Formula: see text] except the origin and give global dynamics with isolated equilibria on the sphere. Finally, we consider the persistence of the attractive invariant sphere under the perturbation induced by linear multiplicative Wiener noise and focus on if stochastic bifurcations occur. It is shown that suitable noise intensity can destroy the sphere and lead to bifurcations of stationary measures.

Source: Stochastics and Dynamics

DOI: 10.1142/s0219493725500388

Authors: Dongmei Xiao, Shengnan Yin, Chenwan Zhou

Institutions: Shanghai Jiao Tong University, New York University Shanghai

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G6478740030