In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel–Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic equation. For the Hopf bifurcation analysis, th...

We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequen...

| A novel observer for tracking and identifying a chaotic system with time-varying bifurcation parameters via an observation signal contaminated by additive white Gaussian noise (AWGN) is developed in this paper. It is realized by an adaptive algorithm which takes advantage of the good approximation capability of the Radial Basis Function (RBF) neural network and the ability of the Extended Kal...

This paper presents a detailed bifurcation analysis of multi-parameter power systems. Equilibrium points are used to evaluate the system eigenvalues and obtain different bifurcation diagrams for two sample systems. The paper studies the influence of hard-limits, AVR droop and reactive power compensation on the local bifurcations of the test systems, using detailed generator models. The stabili...

This paper analyzes the genericity of bifurcations of one-parameter families of smooth (C1) vector …elds that are embedded in an underlying multidimensional parameter space. Bifurcations with crossing equilibrium loci are called “split bifurcations.”They include, for example, the pitchfork bifurcation and the transcritical bifurcation in one-dimensional systems. In a regular parameter space whe...