Peculiarities of Synchronization of Randomly Interlayer Coupled Networks of Chaotic Maps
Elena V. Rybalova1, Galina I. Strelkova1.
1Saratov State University, Saratov, Russia
Abstract
The study of the dynamics of multicomponent and multilayer networks, as well as the evolution of spatiotemporal structures within them, is important for understanding the behavior of many real systems. In particular, synchronization phenomena in complex networks play a significant role in physics, chemistry, neuroscience, sociology, communication systems, power grids, and transport networks.
Various forms of synchronization have been identified in complex networks, including complete, partial, cluster, forced, mutual, explosive, and relay synchronization. Among the structures associated with partial synchronization, the most prominent are chimera states and solitary states. These regimes represent intermediate stages between complete synchronization and incoherent dynamics. Numerous studies have investigated their interaction under different types of interlayer coupling, including constant, sparse, delay, and noise-modulated coupling. However, randomly distributed interlayer coupling in space and randomly blinking coupling remain insufficiently explored.
In this work, we investigate a two-layer network with heterogeneous static and dynamic interlayer couplings. Individual nodes are described by Hénon–Lozi maps, which allow the formation of different spatiotemporal regimes, including chimera and solitary states. The first layer is initialized in a solitary state, whereas the second layer exhibits a chimera state. Interlayer coupling is activated randomly according to different temporal and spatial scenarios.
Synchronization is analyzed numerically using both randomly distributed and specially prepared initial conditions. The study demonstrates that the proposed network can achieve synchronization in solitary or chimera regimes depending on the characteristics of the interlayer coupling, revealing the influence of different random coupling strategies on the stability and synchronization of spatiotemporal structures.
Speaker
Vladislav M. Averyanov
Saratov State University
Russia
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