Abstract
A new phenomenon of the chimera states cloning in a large two-layer multiplex network with short-term couplings has been discovered and studied. For certain values of strength and time of multiplex interaction, in the initially disordered layer, a state of chimera is formed with the same characteristics (the same average frequency and amplitude distributions in coherent and incoherent parts, as well as an identical phase distribution in coherent part), as in the chimera which was set in the other layer. The mechanism of the chimera states cloning is examined. It is shown that the cloning is not related with synchronization, but arises from the competition of oscillations in pairs of oscillators from different layers.
Highlights
Study of the formation of chimera states, i.e., peculiar types of hybrid states consisting of oscillators with coherent and incoherent behavior is one of the hot problems of the modern non-linear dynamics
For certain values of strength and time of multiplex interaction, in the second layer, a chimera state is formed with the same average frequency and amplitude distributions in coherent and incoherent parts, as well as an identical phase distribution in coherent part, as in the chimera which was set in first layer
When the chimera state existing in one of the layers interacts for a while with oscillations of the other layer having a random distribution of phases, the same chimera state appears in the latter layer
Summary
Study of the formation of chimera states, i.e., peculiar types of hybrid states consisting of oscillators with coherent and incoherent behavior is one of the hot problems of the modern non-linear dynamics. We presented an example [43] of a two-layer multiplex network with seven oscillators in each layer where due to short-term interaction, one more chimera is emerged which is identical to the initial one (excluding the phase distribution of the incoherent part). We called this effect the chimera states cloning. We generalize the results of Dmitrichev et al [43] for the case of a multiplex network with an arbitrary dimension of the layer and give a theoretical justification for the cloning effect based on the study of the fast-slow dynamics of the model using the methods of Geometric Singular Perturbation Theory (GPST) [44, 45]
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