Abstract
Geometrical criterion is a flexible method to be applied to a type of delay differential equations with delay dependent coefficient. The criterion is used to solve roots attribution of the related characteristic equation in complex plane effectively by introducing a new parameter skillfully. An extended geometrical criterion is developed to compute the stability of DDEs with two time delays. It is found that stability switching phenomena arise while equilibrium solution loses its stability and becomes unstable, then retrieve its stability again. Hopf bifurcation and the bifurcating periodic solution is analyzed by applying central manifold reduction method. The novel dynamical behaviors such as periodical solution bifurcating to chaos are discovered by using numerical simulation method.
Highlights
As is well known, the issue of delay differential equations has aroused a big attention from a rather diverse group of scientist since its application widely in many fields of science and engineering
Geometrical criterion is a flexible method to be applied to a type of delay differential equations with delay dependent coefficient
The stability analysis of system is ubiquitous since bifurcation behavior of equilibrium and periodic solution can change system dynamics dramatically as varying time delay (Gourley & Kuang, 2004; Wang & Hu, 1999; Cooke et al, 1999)
Summary
The issue of delay differential equations has aroused a big attention from a rather diverse group of scientist since its application widely in many fields of science and engineering. The stability analysis of system is ubiquitous since bifurcation behavior of equilibrium and periodic solution can change system dynamics dramatically as varying time delay (Gourley & Kuang, 2004; Wang & Hu, 1999; Cooke et al, 1999). A notable example was the work of Aiello and Freedman on a single species model with two growth stages and delay dependent coefficients On another respect, population movement is the common habits that happened on some living beings, such as fishes or birds, for example, population partly migrate from the birth place to another habitat for finding plentiful foods, and return back after a long period.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
