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Journal of Applied Nonlinear Dynamics 9(4) (2020) 567--574 | DOI:10.5890/JAND.2020.12.004

Ankan Pandey$^1$ , Mainak Mitra$^{2}$, A Ghose-Choudhury$^{3}$, Partha Guha$^{1}$

$^1$ SN Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700106, India

$^2$ Ramakrishna Mission Residential College (Autonomous) Narendrapur, Kolkata-700103, West Bengal, India

$^3$ Department of Physics, Diamond Harbour Women's University, Sarisha, West Bengal 743368, India

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Abstract

We investigate the dynamics of a delay differential coupled Duffing-Van der Pol oscillator equation. Using the Lindstedt's method, we derive the in-phase mode solutions and then obtain the slow flow equations governing the stability of the in-phase mode by employing the two variable perturbation method. We solve the slow flow equations using series expansion and obtain conditions for Hopf bifurcation and studied stability of the in-phase mode. Finally, we studied stability and bifurcations of the origin. Our interest in this system is due to the fact that it is related to the coupled laser oscillators.

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