Complex dynamics in biological systems arising from multiple limit cycle bifurcation. (1st January 2016)

• Record Type: Journal Article
• Authors: Yu, P.; Lin, W.
• Is Part Of: Journal of biological dynamics. Volume 10(2016)
• Page Start: 263
• Page End: 285
• Publication Date: 2016-01-01
• Subjects: Dynamical system -- epidemic model -- predator–prey model -- stability -- Hopf bifurcation -- limit cycle -- normal form; 92D30 -- 37L10 -- 37N25; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2016.1166270
• Languages: English
• ISSNs: 1751-3758

Abstract

ABSTRACT: In this paper, we study complex dynamical behaviour in biological systems due to multiple limit cycles bifurcation. We use simple epidemic and predator–prey models to show exact routes to new types of bistability, that is, bistability between equilibrium and periodic oscillation, and bistability between two oscillations, which may more realistically describe the real situations. Bifurcation theory and normal form theory are applied to investigate the multiple limit cycles bifurcating from Hopf critical point.