Controlling Chaos and Bifurcations in Discrete-Time Population Models

Chaos in Discrete Structured Population Models

We prove analytically the existence of chaotic dynamics in some classical discrete-time age-structured population models. Our approach allows us to estimate the sensitive dependence on the initial conditions, regions of initial data with chaotic behavior, and explicit ranges of parameters for which the considered models display chaos. These properties have important implications for evaluating ...

Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use n...

Dynamic Complexity in Discrete - Time Population Models

Grazing Bifurcations and Chaos of a Hydraulic Engine Mount

The constitutive relationships of the rubber materials that act as the main spring of a hydraulic engine mount are nonlinear. In addition to material induced nonlinearity, further nonlinearities may be introduced by mount geometry, turbulent fluid behavior, temperature, boundary conditions, decoupler action, and hysteretic behavior. In this research all influence the behavior of the system only...

Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two paramet...