Spiral wave chimera-like transient dynamics in three-dimensional grid of diffusive ecological systems

TL;DR

This paper investigates the emergence and transition of spiral wave chimera-like transient patterns in three-dimensional ecological systems with prey-predator interactions, revealing how these patterns evolve over time and under different diffusion conditions.

Contribution

It introduces the first analysis of transient spiral chimera-like states in 3D ecological systems with prey-predator dynamics, highlighting their transition mechanisms and long-term behavior.

Findings

Transient spiral chimera-like patterns observed in 3D ecological models.

Transitions from chimera-like states to synchronized or desynchronized patterns.

Duration of transient states depends on diffusion and initial conditions.

Abstract

In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional medium through local diffusion. We explore the transition scenarios among the several collective dynamical behaviors together with transient spiral wave chimera-like states and investigate the long time behavior of these states. The transition from the transient spiral chimera-like pattern to the long time synchronized or desynchronized pattern appears through the deformation of the incoherent region of the spiral core. We discuss the transient dynamics under the influence of the species diffusion at different time instants. By calculating the instantaneous strength of incoherence of the populations, we estimate the duration of the transient dynamics characterized by the persistence of the chimera-like spatial coexistence of coherent and incoherent patterns over the spatial domain. We generalize our observations on the transient dynamics in three-dimensional grid of diffusive ecological systems by considering two different prey-predator systems.