Modified post-bifurcation dynamics and routes to chaos from double-Hopf bifurcations in a hyperchaotic system

Double Hopf Bifurcations and Chaos of a Nonlinear Vibration System

A double pendulum system is studied for analyzing the dynamic behaviour near a critical point characterized by nonsemisimple 1:1 resonance. Based on normal form theory, it is shown that two phase-locked periodic solutions may bifurcate from an initial equilibrium, one of them is unstable and the other may be stable for certain values of parameters. A secondary bifurcation from the stable period...

Double Singularity-induced Bifurcation Points and Singular Hopf Bifurcations

We explore the singularity-induced bifurcation and singular Hopf bifurcation theorems and the degeneracies that arise when Newton’s Laws are coupled to Kirchhoff’s Laws. Such models are used in the electrical engineering literature to describe electrical power systems and they can take the form of either an index-1 differential-algebraic equation (DAE) or a singularly perturbed ordinary differe...

Double Hopf Bifurcations

Bifurcation analysis and dynamics of a Lorenz –type dynamical system 

./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcati...

Bifurcation Dynamics in Control Systems

This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential equations and delayed differential equations. In particular, bifurcations related to double Hopf, combination of double zero and Hopf, and chaos are studied in detail. Center manifold theory and normal form theory are applied to simplify the analysis. Exp...