Synchronization of spatially moving delay coupled chaotic oscillators

Synchronization phenomenon in different systems is analysed in this thesis. First, results of the paper 'From Phase to Lag Synchronization in Coupled Chaotic Oscillators PRL, Michael G. Rosenblum,* Arkady S. Pikovsky, and Jurgen Kurths' are reproduced and the Fortran program for calculating Leyapunov exponents is given in Appendix 1. In the second part synchronization in an ensemble of oscillators in a finite two dimensional space is studied. The oscillators move in space in a random manner and interaction is governed by their spatial movement and their vision. The coupling interaction or signal travels with a finite speed which leads to delayed coupling and so this becomes a time delayed system. This is an extension of the work done by Lavneet Janagal and P. Parmananda in their paper ‘Synchronization in an ensemble of spatially moving oscillators with linear and nonlinear coupling schemes’ in which they studied Synchronization in an ensemble of oscillators with an infinite speed of coupling interaction. Some of their work is reproduced here and a Fortran program is given in Appendix 2. Then the extension to finite coupling interaction speed is described and the respective Fortran code is given in Appendix 3. The major results found by introduction of time delayed coupling are that the extent of synchronization was found to decrease with increasing vision instead of increasing as is the case with infinite coupling interaction speed for very small interaction speed. Also the amplitude of oscillation decreased with decreasing interaction speed