Work

Attractivity with asymptotic phase of local center manifolds and an application to one-parameter bifurcation for integral equations with infinite delay

Year: 2025

Type: article

Abstract: For autonomous C 1 -smooth integral equations with infinite delay, exponential attractivity with asymptotic phase of the local center manifolds of the equilibrium 0 , together with a reduction principle, is proved by means of a dynamical systems approach based on the variation-of-constants formula in the phase space established in [Funkcial. Ekvac. 55(2012), 479–520]. As its application to one-parameter family of integral equations, it is also shown that saddle-node and pitchfork bifurcations occur when the equilibrium 0 (the zero solution) of the linearized equation changes its stability properties.

Source: Electronic journal of qualitative theory of differential equations

DOI: 10.14232/ejqtde.2025.1.12

Authors: Hideaki Matsunaga, Kouichi Murakami, Yutaka Nagabuchi

Institutions: Osaka Metropolitan University, Tokushima University, Okayama University of Science

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Awards: The effect of delay on the asymptotic properties of differential equations, The effect of delay on the asymptotic properties of solutions of difference equations