We present a family of unimodal maps, arising from a simple queueing model, which exhibits reverse bifurcations. We compare and contrast this with bifurcations occurring in the well-known logistic family of unimodal quadratic maps.

Analysis of saddle-node and Hopf bifurcations in IFOC drives due to errors in the estimate of the rotor time constant is presented. Experimental results showing such bifurcations are given and guidelines for drive commissioning are derived from these results.

A formal framework for the analysis of Hopf bifurcations in delay differential equations with a single time delay is presented. Closed-form linear algebraic equations are determined and the criticality of bifurcations is calculated by normal forms.

The study of the piecewise linear differential systems goes back to Andronov, Vitt and Khaikin in 1920’s, nowadays such still continue receive attention many researchers mainly due their applications. We discontinuous formed by two centers separated a nonregular straight line. provide upper bounds for maximum number limit cycles that these can exhibit we show are reached. Hence, solve extended ...

In this paper, a three dimensional mathematical model for HTLV-1infection with intracellular delay and immune activation delay is investigated.By applying the frequency domain approach, we show that time delays candestabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and sta-ble or unstable periodic oscillations. At the end, numerical simulations areillustrated.

The normal forms of Hopf and generalized Hopf bifurcations have been extensively studied, and obtained using the method of normal form theory and many other different approaches. It is well known that if the normal forms of Hopf and generalized Hopf bifurcations are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal form. In this paper, three theorem...

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use continuation from the limit to study their bifurcations. We find a bound on the parameter range for which the Hénon map exhibits a complete binary horseshoe as well as a subshift of finite type. We classify homoclinic bifurcations, and study tho...

The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis in a suitable frequency band. Moreover, due to the existing connection between limit cycle bifurcations and rout...

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...