Chimera states in multiplex networks: Chameleon-like across-layer synchronization

The physiology of coordination: self-resolving diverse affinities via the sparse order in relevant noise

Living systems at any given moment enact a very constrained set of end-directed and contextually appropriate actions that are self-initiated from among innumerable possible alternatives. However, these constrained actions are not necessarily because the system has reduced its sensitivities to themselves and their surroundings. Quite the contrary, living systems are continually open to novel and unanticipated stimulations that require a physiology of coordination. To address these competing demands, this paper offers a novel heuristic model informed by neuroscience, systems theory, biology and sign study to explain how organisms situated in diverse, complex and ever-changing environments might draw upon the sparse order made available by 'relevant noise'. This emergent order facilitates coordination, habituation and, ultimately, understanding of the world and its relevant affordances. Inspired by the burgeoning field of coordination dynamics and physiologist Denis Noble's concept of 'biological relativity', this model proposes a view of coordination on the neuronal level that is neither sequential nor stochastic, but instead implements a causal logic of phasic alignment, such that an organism's learned and inherited sets of diverse biological affinities and sympathies can be resolved into a continuous and complex range of patterns that will implement the kind of novel orientations and radical generativity required of such organisms to adaptively explore their environments and to learn from their experiences.

Complete synchronization of three-layer Rulkov neuron network coupled by electrical and chemical synapses

This paper analyzes the complete synchronization of a three-layer Rulkov neuron network model connected by electrical synapses in the same layers and chemical synapses between adjacent layers. The outer coupling matrix of the network is not Laplacian as in linear coupling networks. We develop the master stability function method, in which the invariant manifold of the master stability equations (MSEs) does not correspond to the zero eigenvalues of the connection matrix. After giving the existence conditions of the synchronization manifold about the nonlinear chemical coupling, we investigate the dynamics of the synchronization manifold, which will be identical to that of a synchronous network by fixing the same parameters and initial values. The waveforms show that the transient chaotic windows and the transient approximate periodic windows with increased or decreased periods occur alternatively before asymptotic behaviors. Furthermore, the Lyapunov exponents of the MSEs indicate that the network with a periodic synchronization manifold can achieve complete synchronization, while the network with a chaotic synchronization manifold can not. Finally, we simulate the effects of small perturbations on the asymptotic regimes and the evolution routes for the synchronous periodic and the non-synchronous chaotic network.