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NJIT Mathematical Biology Seminar

Tuesday, January 18, 2011, 2:30pm
Cullimore Hall 611
New Jersey Institute of Technology

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Scenarios of generalized synchronizationi in chaotically driven systems

Thounaojam Umeshkanta Singh

School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India

Generalized synchronization (GS) is one of the most common ways in which temporal correlations between systems can arise. When a nonlinear system is driven by a chaotic, quasiperiodic or stochastic drive, if the response has a unique functional dependence on the drive, then the response is said to be in generalized synchrony with the drive. Depending on whether the function is differentiable or not, GS is classified as either strong or weak. Quasiperiodically driven systems have been studied extensively in the context of strange nonchaotic attractors (SNAs): they provide an example of weak GS.

In this talk, I will discuss the scenarios of generalized synchronization in chaotically driven systems. Weak GS can occur via distinct bifurcation routes with parallels to the routes through which SNAs are formed in quasiperiodically driven systems. The limit sets of the dynamics for weak GS are nonchaotic--the Lyapunov exponent is nonpositive--and are geometrically strange. Dynamical transitions between strong and weak GS can be characterized by quantitative measures. They show contrasting sensitivity to parametric variation and have distinct distributions of finite-time Lyapunov exponents. Generalized synchronization is a robust process, and the existence of definitive mechanisms suggest applications in control and secure communications. The generation of stable aperiodic dynamics in weak GS regime has also been a major objective in the study of driven dynamical systems to understand the manner in which natural systems maintain stability and rhythms.