Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control

doi:10.1088/1674-1056/ac1b83

Abstract A fractional-order difference equation model of a third-order discrete phase-locked loop (FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.

Keywords: discrete Josephson junction fractional order chaos impulse control chimera

Received: 16 March 2021
Revised: 11 June 2021
Accepted manuscript online: 07 August 2021

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the Center for Nonlinear Systems, Chennai Institute of Technology, India (Grant No. CIT/CNS/2020/RD/061).

Corresponding Authors: Karthikeyan Rajagopal
E-mail: rkarthiekeyan@gmail.com

Cite this article:

Karthikeyan Rajagopal, Anitha Karthikeyan, and Balamurali Ramakrishnan Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control 2021 Chin. Phys. B 30 120512

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Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control

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