We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of Hénon maps. It is known that coexisting basins of attraction lead to a hysteretic behaviour in the...
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We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of Hénon maps. It is known that coexisting basins of attraction lead to a hysteretic behaviour in the diagrams of the density of states as a function of a varying parameter. Chimera states, for which coherent and incoherent domains occur simultaneously, emerge as a consequence of the coexistence of basin of attractions for each state. Consequently, the distribution of chimera states can remain invariant by a parameter change, as well as it can suffer subtle changes when one of the basins ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states, respectively. This way, we show that the density of chimera states can be not only moderately sensitive but also highly sensitive to initial conditions. This chimera's dilemma is a consequence of the fractal and riddled nature of the basins boundaries. Coupled dynamical systems have been used to describe the behaviour of real complexsystems, such as power grids, neuronal networks, economics, and chemical reactions. Furthermore, these systems can exhibit various kinds of interesting nonlinear dynamics, e.g. synchronisation, chaotic oscillations, and chimera states. The chimera state is a spatio-temporal pattern characterised by the coexistence of coherent and incoherent dynamics. It has been observed in a great variety of systems, ranging from theoretical and experimental arrays of oscillators, to in phenomena such as the unihemispheric sleep of cetaceans. We study the chimera state in a circulant network of Hénon maps, seeking to determine how the density of states in the network depends on the system parameters and the initial conditions. We have found that, as expected, the density of states might be inva
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