John, Manu Punnen; Dr.Nandakumaran,V M(Cochin University of Science & Technology, January , 2009)
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Abstract:
Nonlinear dynamics has emerged into a prominent area of research in the past few Decades.Turbulence, Pattern formation,Multistability etc are some of the important areas of research in nonlinear dynamics apart from the study of chaos.Chaos refers to the complex evolution of a deterministic system, which is highly sensitive to initial conditions. The study of chaos theory started in the modern sense with the investigations of Edward Lorentz in mid 60's. Later developments in this subject provided systematic development of chaos theory as a science of deterministic but complex and unpredictable dynamical systems. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. Here we introduce the concept of noise, and two
familiar types of noise are discussed. The classifications and representation of white
and colored noise are introduced. Based on this we introduce the concept of randomness that we deal with as a variant of the familiar concept of noise. The dynamical
systems introduced are the Rossler system, directly modulated semiconductor lasers
and the Harmonic oscillator. The directly modulated semiconductor laser being not
a much familiar dynamical system, we have included a detailed introduction to its
relevance in Chaotic encryption based cryptography in communication. We show that the effect of a fluctuating parameter mismatch on synchronization is to destroy the synchronization. Further we show that the relation between synchronization error and timescales can be found empirically but there are also cases
where this is not possible. Studies show that under the variation of the parameters, the system becomes chaotic, which appears to be the period doubling route to chaos.
Description:
International School of Photonics, Cochin University of Science and Technology