S K Dana
Articles written in Pramana – Journal of Physics
Volume 64 Issue 3 March 2005 pp 443-454
We report our experimental observations of the Shil’nikov-type homoclinic chaos in asymmetry-induced Chua’s oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations. The asymmetry is introduced in the circuit by forcing a DC voltage. For a selected asymmetry, when a system parameter is controlled, we observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of periodic mixed-mode oscillations interspersed by chaotic states. Moreover, we observed two intermediate bursting regimes. Experimental evidences of homoclinic chaos are verified with PSPICE simulations.
Volume 84 Issue 2 February 2015 pp 203-215
A design of coupling is proposed to control partial synchronization in two chaotic oscillators in a driver–response mode. A control of synchrony between one response variables is made possible (a transition from a complete synchronization to antisynchronization via amplitude death and vice versa without loss of synchrony) keeping the other pairs of variables undisturbed in their pre-desired states of coherence. Further, one of the response variables can be controlled so as to follow the dynamics of an external signal (periodic or chaotic) while keeping the coherent status of other variables unchanged. The stability of synchronization is established using the Hurwitz matrix criterion. Numerical example of an ecological foodweb model is presented. The control scheme is demonstrated in an electronic circuit of the Sprott system.
Volume 84 Issue 2 February 2015 pp 229-235
We report the existence of chimera states in an assembly of identical nonlinear oscillators that are globally linked to each other in a simple planar cross-coupled form. The rotational symmetry breaking of the coupling term appears to be responsible for the emergence of these collective states that display a characteristic coexistence of coherent and incoherent behaviour. The finding, observed in both a collection of van der Pol oscillators and chaotic Rössler oscillators, further simplifies the existence criterion for chimeras, thereby broadens the range of their applicability to real-world situations.
Volume 94, 2020
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