Various bifurcations exist in nonlinear dynamical systems such as complex circuits, networks, and devices. Bifurcations can be important and beneficial if they are under appropriate control. Bifurcation control and anti-control deal with modification of system bifurcative characteristics by a designed control input. Typical bifurcation control and anti-control objectives include delaying the on...

This is an overview of our recent works on the global bifurcation analysis multi-parameter polynomial dynamical systems. In particular, using bifurcation-geometric approach, we study dynamics and solve problem maximum number distribution limit cycles in a Euler–Lagrange–Liénard-type mechanical system. We also consider rational endocrine system by carrying out reduced planar quartic Topp system,...

This paper is devoted to the existence and stability analysis of limit cycles in a delayed mathematical model for the economy growth. Specifically the Solow model is further improved by inserting the time delay into the logistic population growth rate. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when...

We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary...

The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold. It is based on truncated normal form equations, which have a phase-shift symmetry yielding a further reduction to a ...

this paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. this pde can be transformed to an ode by means of a galerkin method. here by using a criterion which is closely related to the routh-hurwitz criterion, we investigate the mentioned transformed ode from hopf bifurcation point of view. in fact we obtain a region for existence of simple hop...