Relaxation Oscillations in Predator–Prey Systems

2021 ◽  
Author(s):  
Shangbing Ai ◽  
Yingfei Yi
Keyword(s):  
Relaxation Oscillations ◽  
Predator Prey

Nonclassical Relaxation Oscillations in a Mathematical Predator–Prey Model

2020 ◽  
Vol 56 (8) ◽  
pp. 976-992
Author(s):  
S. D. Glyzin ◽  
A. Yu. Kolesov ◽  
N. Kh. Rozov
Keyword(s):  
Relaxation Oscillations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED GENERALIZED LIENARD SYSTEMS WITH NON-GENERIC TURNING POINTS

2017 ◽  
Vol 22 (3) ◽  
pp. 389-407 ◽  
Author(s):  
Huan Hu ◽  
Jianhe Shen ◽  
Zheyan Zhou ◽  
Zhonghui Ou
Keyword(s):  
Turning Point ◽  
Singularly Perturbed ◽  
Relaxation Oscillations ◽  
Biological Models ◽  
Asymptotic Behaviors ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Liénard Systems ◽  
Analysis Technique ◽  
Specific Parameter

Based on the asymptotic analysis technique developed by Eckhaus [Lecture Notes in Math., vol. 985, pp 449-494. Springer, Berlin, 1983], this paper aims to study the existence and the asymptotic behaviors of relaxation oscillations of regular and canard types in a singularly perturbed generalized Lionard system with a non-generic turning point. The singularly perturbed Lionard system considered in this paper is very general and numerous real world models like some biological ones can be rewritten in the form of this system after a series of transformations. Under certain conditions, we rigorously prove the existence of regular relaxation oscillations and canard relaxation oscillations under the specific parameter conditions. As an application, two biological models, namely, a FitzHugh-Nagumo model and a twodimensional predator-prey model with Holling-II response are studied, in which, the existence of regular relaxation oscillations and canard relaxation oscillations as well as the bifurcation curves are obtained.

scholarly journals Relaxation oscillations in a class of predator–prey systems

2003 ◽  
Vol 188 (1) ◽  
pp. 306-331 ◽  
Author(s):  
Weishi Liu ◽  
Dongmei Xiao ◽  
Yingfei Yi
Keyword(s):  
Relaxation Oscillations ◽  
Predator Prey
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