Work

Invariant Sets, Global Dynamics, and the Neimark–Sacker Bifurcation in the Evolutionary Ricker Model

Year: 2024

Type: article

Abstract: In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables to both reduce the number of parameters as well as bring symmetry to the isoclines of the mapping. With this new model, we demonstrate the existence of a forward invariant and globally attracting set where all the dynamics occur. In this set, the model possesses two symmetric fixed points: the origin, which is always a saddle fixed point, and an interior fixed point that may be globally asymptotically stable. Moreover, we observe the presence of a supercritical Neimark–Sacker bifurcation, a phenomenon that is not present in the original non-evolutionary model.

Source: Symmetry

DOI: 10.3390/sym16091139

Authors: Rafael Luís, Brian Ryals

Institutions: Instituto Superior Técnico, Universidade Técnica de Lisboa, Universidade da Madeira, California State University, Bakersfield

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $2,728

OpenAlex ID: W4402127705

FWCI: 1.128

Cites: 43

Cited by: 3

Related to: 10