Dear Colleagues,

Spatio-temporal pattern formation resulting from the heterogeneous distribution of interacting populations are capable of producing a wide variety of patterns. The heterogeneous distributions themselves can be classified as stationary patterns, oscillatory patterns, spatio-temporal chaotic patterns, and so on. Nonlinear parabolic partial differential equations (for single or multi-species interaction with one or higher dimensional space) are the basic modelling approach to study the pattern formation for single or multi-species population growth. Several mathematical aspects are involved in the investigation of spatio-temporal pattern formation, namely: existence of travelling and periodic travelling waves, Turing instability, Turing–Hopf bifurcation, invasion, wave of invasion, wave of chaos, etc. Existence of various types of spatial patterns can describe the size and nature of population patches, changes of habitats, movement of the individuals or groups of individuals from one location to another, invasion of new species and so on. These are examples from an expanding list of interpretations of the spatial patterns.

Recently, researchers have become interested in studying various types of stationary and non-stationary patterns produced by the models with cross-diffusion terms, nonlocal interaction terms, and advection terms, along with various types of boundary conditions. The basic mechanisms behind the generation of various patterns and their bifurcations are still an active area of research.

The aim of this special issue is to present state-of-the-art research work in the area of spatial pattern formation by interacting populations, to enhance the understanding of the basic mechanisms responsible for various types of pattern formation and their ecological interpretations. Authors are invited to submit their original and review papers devoted to patterns and waves in the context of ecology and cell population dynamics.

Prof. Dr. Vitaly Volpert
Dr. Malay Banerjee
Dr. Moitri Sen
Guest Editors

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• spatial pattern
• travelling wave
• Turing instability
• Turing–Hopf bifurcation
• invasion
• spatio-temporal chaos