Stability and Hopf bifurcation analysis of the Mackey-Glass and Lasota equations
Time delays are an integral part of various physiological processes.In this paper,we analyse two models for physiological systems: the Mackey-Glass and Lasota equations.We first exhibit a sufficient condition to ensure local stability,and then outline the associated necessary and sufficient condition for stability.Using a non-dimensional bifurcation parameter,we then highlight that stability will be lost via a Hopf bifurcation.We also explicitly characterise the type of the Hopf bifurcation using Poincar′e normal forms and the center manifold theory.The theoretical analysis is complemented with some numerical examples,stability charts and bifurcation diagrams.
Physiological processes Mackey-Glass equation Lasota equation stability Hopf bifurcation
Sreelakshmi Manjunath Gaurav Raina
Department of Electrical Engineering,Indian Institute of Technology Madras,Chennai 600 036,India
国际会议
长沙
英文
2076-2082
2014-05-31（万方平台首次上网日期，不代表论文的发表时间）