https://doi.org/10.1140/epjst/e2014-02137-7
Regular Article
Chimera states in a two–population network of coupled pendulum–like elements
1 Department of Mathematics, University of Patras, Patras, Greece
2 Department of Electrical and Computer Engineering, University of Patras, Patras, Greece
3 National Center for Scientific Research “Demokritos”, Athens, Greece
4 Cognitive Engineering Lab, Singapore Institute for Neuroengieering (SINAPSE), National University of Singapore, Singapore
a e-mail: tassos50@otenet.gr
Received: 3 March 2014
Revised: 18 March 2014
Published online: 28 April 2014
More than a decade ago, a surprising coexistence of synchronous and asynchronous behavior called the chimera state was discovered in networks of nonlocally coupled identical phase oscillators. In later years, chimeras were found to occur in a variety of theoretical and experimental studies of chemical and optical systems, as well as models of neuron dynamics. In this work, we study two coupled populations of pendulum-like elements represented by phase oscillators with a second derivative term multiplied by a mass parameter m and treat the first order derivative terms as dissipation with parameter ∊>0. We first present numerical evidence showing that chimeras do exist in this system for small mass values 0<m≪1. We then proceed to explain these states by reducing the coherent population to a single damped pendulum equation driven parametrically by oscillating averaged quantities related to the incoherent population.
© EDP Sciences, Springer-Verlag, 2014
