Synchronization State in the Coupled Van Der Pol Oscillators within a Small Invariant Subspace
DOI:
https://doi.org/10.29304/jqcsm.2025.17.11987Keywords:
Van der Pol model, Damping parameter, Coupling strength, Synchronization, Limit cycleAbstract
This study aims to analyze the dynamics of trajectories in a system of Van der Pol with the coupled oscillator. The control parameters considered are damping and coupling strength. We focus on study the behaviour of this system within a specific small invariant subspace. It is used phase difference to reduce the dimension of this system into two dimensions. Then, the Jacobian matrix is computed eigenvalues in order to determine the stability of equilibrium point. this work specifically discovers the effects the damping and coupling strength parameters to emerge synchronization states. additionally, it investigates how change the value of damping parameter influence on the system's energy.
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Cai, W. and Sen, M., Synchronization of thermostatically controlled first-order systems. International Journal of Heat and Mass Transfer, (2008), 51(11-12), pp.3032-3043.
Kawahara, T., Coupled van der Pol oscillators a model of excitatory and inhibitory neural interactions. Biological cybernetics, (1980), 39(1), pp.37-43.
Fukuda, H., Tamari, N., Morimura, H. and Kai, S., Entrainment in a chemical oscillator chain with a pacemaker. The Journal of Physical Chemistry A, (2005), 109(49), pp.11250-11254.
Woafo, P. and Kadji, H.E., Synchronized states in a ring of mutually coupled self-sustained electrical oscillators. Physical Review E, (2004), 69(4), p.046206.
Pastor-Diaz, I. and López-Fraguas, A., Dynamics of two coupled van der Pol oscillators. Physical Review E, (1995), 52(2), p.1480.
VanderPol,B.,LXXXVIII. “On relaxation-oscillations”.The London, Edinburgh, and Dublin Philo- sophical Magazine and Journal of Science, (1926), 2(11), pp.978-992.
Strogatz, S.H., From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, (2000), 143(1-4), pp.1-20.
Gholizade-Narm,H.,Azemi,A.andKhademi,M., Phasesynchronizationandsynchronization frequency of two-coupled van der Pol oscillators with delayed coupling. Chinese Physics B,(2013), 22(7), p.070502.
Pikovsky, A., Rosenblum, M., Kurths, J. and Synchronization, A., A universal concept in nonlinear sciences. Self, (2001), 2, p.3.
Acebro ́n, J.A., Bonilla, L.L., Pe ́rez Vicente, C.J., Ritort, F. and Spigler, R., The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of modern physics, (1926), 77(1), pp.137-185.
Kuramoto, Y., Chemical oscillations, waves, and turbulence. (1984), 8, p.156.
Ermentrout, B. and Terman, D.H., 2010. Mathematical foundations of neuroscience, (2010), vol. 35, pp. 331-367. New York: Springer.
Mary Thoubaan and Peter Ashwin. Existence and stability of chimera states in a minimal system of phase oscillators. Chaos: An Interdisciplinary Journal of Non-linear Science, (2018), 28(10).
Peter Ashwin and Oleksandr Burylko.Weak chimeras in minimal networks of coupled phase oscillators. Chaos: An Interdisciplinary Journal of Nonlinear Science,(2015), 25(1).
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