Spiral dynamics in oscillatory bilayer systems with an inhomogeneous inter-layer coupling

Spiral dynamics in the oscillatory bilayer system with an inhomogeneous inter-layer coupling and a spiral-resting initial state are studied, where the square coupled patches are arranged into a square lattice array. Depending on the patch side length, the lattice space and the coupling strength, different dynamical behaviors can be observed. The complete synchronization of two spiral waves easily occurs when the coupled areas occupy a larger proportion in the whole region. The bilayer system can also show several typical asynchronous patterns, where the spiral with the closed tip path, the spiral with the complex phase shifting, the state with multiple spirals, the spiral turbulence, and the non-smooth traveling pulses can be formed in the single layers of the bilayer. The variable difference functions are computed, and three types of asymptotic behaviors are identified, which include the behaviors of approaching the constant, periodic variation, and aperiodic variation around the constant. These asymptotic behaviors can describe some properties of the bilayer patterns after a transient interval. For example, the variable difference function has a periodical asymptotic behavior when the spiral with the closed tip path is formed in the single layer. The heterogeneity of inter-layer coupling can also induce some complex tip trajectories.

Automated summary

In this study, the spiral dynamics in an oscillatory bilayer system with inhomogeneous inter-layer coupling and a spiral-resting initial state was investigated. It was found that depending on the proportion of coupled areas and the coupling strength, complete synchronization of two spiral waves as well as several asynchronous patterns can be observed.