Recent researches in network science demonstrate the coexistence of different types of interactions among the individuals within the same system. A wide range of situations appear in ecological and neuronal systems that incorporate positive and negative interactions. Also, there are numerous examples of systems that are best represented by the multiplex configuration. The present article investigates a possible scenario for the emergence of a newly observed remarkable phenomenon named as solitary state in coupled dynamical units in which one or a few units split off and behave differently from the other units. For this, we consider dynamical systems connected through a multiplex architecture in the presence of both positive and negative couplings. We explore our findings through analysis of the paradigmatic FitzHugh-Nagumo system in both equilibrium and periodic regimes on the top of a multiplex network having positive inter-layer and negative intra-layer interactions. We further substantiate our proposition using a periodic Lorenz system with the same scheme and show that an opposite scheme of competitive interactions may also work for the Lorenz system in the chaotic regime.
Topics
Chimeras
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Other values of these external stimuli will also work in the context of the following observed results on FHN system in equilibrium regime, i.e., one can identify the same dynamical states that we have presented here, provided the two values and are chosen from the two different zones I (region before the Hopf bifurcation) and II (region after the Hopf bifurcation) of the bifurcation diagram [cf. Fig. 2(a)].
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2019
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