Chimera states in coupled sine-circle map lattices

Abstract

Systems of coupled oscillators have been seen to exhibit chimera states, i.e. states where the system splits into two groups where one group is phase locked and the other is phase randomized. In this work, we report the existence of chimera states in a system of two interacting populations of sine circle maps. This system also exhibits the clustered chimera behavior seen earlier in delay coupled systems. Rich spatio-temporal behavior is seen in different regimes of the phase diagram. We carry out a detailed analysis of the stability regimes and map out the phase diagram using numerical and analytic techniques.

Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics

“…Chimera states in a ring network of nonlocally coupled logistic maps were first described by Omelchenko and colleagues. 22 Nayak and Gupte 45 reported on chimera states in two populations of sine-circle maps. The first experimental observation of chimeras in electro-optical coupled map lattices in one and two dimensions was provided by Hagerstrom et al 24 Apart from coupled logistic maps, 22,23,[27][28][29][30][37][38][39][41][42][43][44] chimera states were illustrated for coupled Henon maps, 26,[32][33][34]36 sinecircle maps, 45,46 sine-squared maps, 35,44 cosine maps, 24 piecewise linear and logistic maps, 25 and cubic maps.…”

“…22 Nayak and Gupte 45 reported on chimera states in two populations of sine-circle maps. The first experimental observation of chimeras in electro-optical coupled map lattices in one and two dimensions was provided by Hagerstrom et al 24 Apart from coupled logistic maps, 22,23,[27][28][29][30][37][38][39][41][42][43][44] chimera states were illustrated for coupled Henon maps, 26,[32][33][34]36 sinecircle maps, 45,46 sine-squared maps, 35,44 cosine maps, 24 piecewise linear and logistic maps, 25 and cubic maps. 31,39,40 They were found for ring networks with nonlocal coupling, [22][23][24][25][26][28][29][30][31][32][33][34][35][36]39,[41][42]…”

Chimeras confined by fractal boundaries in the complex plane

“…While chimera states were first described 19 and continue to be studied for networks of time-continuous oscillators, an increasing interest is paid to networks of time-discrete maps. Chimera states were found for networks of coupled logistic maps [4][5][6][7][8][9][23][24][25][26][27][28][29][30][31] , Henon maps [10][11][12][13][14][15]21 , cubic maps 7,16,17 , map-based neuron models 18,32 , sine-circle maps [33][34][35] , sine-squared maps 23,26,36 , cosine maps 37 , piecewise linear maps 38 , and piecewise logistic maps 38 . Recently, two populations of quadratic maps with real-valued parameter c were shown to yield a plentitude of dynamics including chimera states 39 .…”