About a three-dimensional autonomous continuous Lorenz-like system. Through the full analysis of equilibrium points, we can derive the parameter condition of Hopf bifurcation; Next we adopt a Washout filter controller designed independently to control the Hopf bifurcation of the system, and the effect of the controller’s parameters on the position of bifurcation point, the bifurcation type, and...

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lamé functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use standard perturbation theory to obtain their evolution away from the bifurcation points. As an application, we deri...

In this paper, we are concerned with the Rose–Hindmarsh model with time delay. By applying the generalized Sturm criterion, a number of imaginary roots of the characteristic equation are classified. The absolutely stable regions for any value of time delay are detected. By the continuous software DDE-Biftool, both the Hopf bifurcation curves and double Hopf bifurcation points are illustrated in...

This paper deals with periodic solutions of the Hamilton equation ẋ(t) = J∇xH(x(t), λ), where H ∈ C2,0(R2n × Rk,R) and λ ∈ Rk is a parameter. Theorems on global bifurcation of solutions with periods 2π j , j ∈ N, from a stationary point (x0, λ0) ∈ R2n × Rk are proved. ∇xH(x0, λ0) can be singular. However, it is assumed that the local topological degree of ∇xH(·, λ0) at x0 is nonzero. For system...

The computation of symmetry-breaking bifurcation points of nonlinear multiparameter problems with Z2 (reflectional) symmetry is considered. The numerical approach is based on recent work in singularity theory, which is used to construct systems of equations and inequalities characterising various types of symmetry-breaking bifurcation points. Numerical continuation methods are then used to foll...