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(a) Two-parameter bifurcation diagram in μ-γ space for α = 0.114, β = 0.003, and d = 0.4; (b) two-parameter bifurcation diagram in α-γ space (for μ = 0.1, β = 0.003, and d = 0.4). (c) Two-parameter bifurcation diagram in β-γ space (for μ = 0.1, α = 0.114, and d = 0.4). (d) Two-parameter bifurcation diagram in α-β space with (solid line) and without filtering (μ = 0.1 and d = 0.4): A decreasing γ suppresses the birhythmic zone.
Effect of filtered feedback on birhythmicity: Suppression of birhythmic oscillation
Effect of filtered feedback on birhythmicity: Suppression of birhythmic oscillation
The birhythmic oscillation, generally known as birhythmicity, arises in a plethora of physical, chemical, and biological systems. In this paper we investigate the effect of filtered feedback on birhythmicity as both are relevant in many living and engineering systems. We show that the presence of a low-pass filter in the feedback path of a birhythmic system suppresses birhythmicity and supports monorhythmic oscillations depending on the filtering parameter. Using harmonic decomposition and energy balance methods we determine the conditions for which birhythmicity is removed. We carry out a detailed bifurcation analysis to unveil the mechanism behind the quenching of birhythmic oscillations. Finally, we demonstrate our theoretical findings in analog simulation with electronic circuit. This study may have practical applications in quenching birhythmicity in several biochemical and physical systems. [Physical Review E, 99, 062210 (2019)]
Effect if Filtering in Coupled Systems :
We report an interesting symmetry-breaking transition in coupled identical oscillators, namely, the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the Turing-type symmetry-breaking transition from amplitude death (i.e., stable homogeneous steady state) to oscillation death (i.e., stable inhomogeneous steady state). This novel transition occurs in the parametric zone of occurrence of rhythmogenesis and oscillation death as a consequence of the presence of local filtering in the coupling path. We consider paradigmatic oscillators, such as Stuart-Landau and van der Pol oscillators, under mean-field coupling with low-pass or all-pass filtered self-feedback and through a rigorous bifurcation analysis we explore the genesis of this transition. Further, we experimentally demonstrate the observed transition, which establishes its robustness in the presence of parameter fluctuations and noise. [Physical Review E, 97, 042218 (2018); arXiv:1803.02138v1 [nlin.CD]].Control of Birhythmicity : Birhythmicity arises in several physical, biological and chemical systems. Although, many control schemes are proposed for various forms of multistability, only a few exist for controlling birhythmicity. We have contributed significant research work on controlling the birhythimicity by self-conjugate coupling scheme [Physical Review E, 94, 042226, 2016; Chaos, 27, 063110, 2017].
Amplitude Death island in coupled hyperchaotic system : The hyperchaotic system, when coupled in direct-indirect coupling scheme gives rise to several interesting scenarios including synchronization and amplitude death. In the present case we find some amplitude death island in the coupled system. The variation of time delay also induces interesting cooperative behavior. [Nonlinear Dynamics, DOI 10.1007/s11071-017-3411-7]
Amplitude death : Oscillation quenching is an emergent and intriguing phenomenon that has been the topic of extensive research in diverse fields such as physics, biology, and engineering. One of the type of oscillation quenching process is amplitude death (AD). In this field we have contributed some pioneering researches: examples include
- Discover a NEW transition route to AD in intrinsic time delay system, namely transition among AD, Generalized {lag, anticipatory} synchronization and complete synchronization. [CHAOS (AIP), Vol. 23, No. 4, 043101, 2013]
Design of chaotic & hyperchaotic delayed dynamical systems : In our laboratory we have invented many delayed dynamical systems that show chaotic and hyperchaotic behavior. Those systems are implemented with off-the-shelf electronic circuits that can be controlled and synchronized for the application purposes. [Nonlinear Dyn. (Springer), Vol. 70 (1), pp. 721-734 ( 2012), Int. J. Bifurcation and Chaos, (World Scientific), 23, 1330020 (2013), Nonlinear Dyn. (Springer), Vol. 83, pp. 2331-2347 (2016)]
Synchronization of hyperchaotic delay dynamical systems : Studies on different synchronization phenomena of time-delayed hyperchaotic systems. Our group reported the FIRST EXPERIMENTAL AND THEORETICAL observation of synchronization in chaotic and hyperchaotic time-delay systems coupled by environmental coupling. [Nonlinear Dynamics (Springer), Vol. 73, pp. 2025-2048. 2013]
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