In this study, a model of active control system with time delay feedback is investigated, and time delays were set in control loop. An efficient method was used to analyze the stability of the system. By solving the characteristic equation, the local stability and the existence of codimension one bifurcation (Hopf bifurcation and fold bifurcation) were obtained. Regarding the time delay as bifu...

and Applied Analysis 3 Define

We study the bifurcation of closed minimal surfaces in Riemannian manifolds through higher order variations of the area functional and relate it to elementary catastrophes.

Article history: Received 30 May 2008 Revised 10 September 2008 Available online 16 October 2008 MSC: primary 35J55, 35B32 secondary 46T20, 58C25, 92D25

A discrete-time financial system is proposed by using forward Euler scheme. Based on explicit Neimark-Sacker bifurcation also called Hopf bifurcation for map criterion, normal form method and center manifold theory, the system’s existence, stability and direction of Neimark-Sacker bifurcation are studied. Numerical simulations are employed to validate the main results of this work. Some compari...