Presentation Information
[SS25-01]New mechanism for generating realistic patterns of patchiness in networked and non-networked Ecological systems
*Ranjit Kumar Upadhyay1 (1. Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad (India))
Keywords:
Wave of chaos,Reaction-diffusion system,Network environment,Hopf-bifurcation,Turing Pattern
Existing textbooks and research monographs on theoretical/mathematical ecology, when addressing its spatial and spatiotemporal dynamics, practically never go beyond the classical Turing scenario of pattern formation. Wave of Chaos (WOC) is an effective mechanism for the propagation of chaotic dynamics in predation and competitive systems. The dynamics of a simple ecological system is described by a system of two reaction-diffusion equations with biologically reasonable non-linearities (logistic growth of the prey, Holling type functional response of the predator). When the reaction terms or local kinetics of the system is oscillatory for a wide class of initial conditions, the evolution of the system leads to the formation of a non-stationary irregular pattern corresponding to spatiotemporal chaos. We show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of ecological systems. These spatial patterns serve as a realistic model for patchiness found in aquatic systems (e.g., marine and oceanic), terrestrial systems and disease dynamics. We also explore the development of spatial patterns in both networked and non-networked environments, specifically comparing the formation of Turing patterns in network framework with those observed in continuous media while considering various network topologies. The combined effects of the fear parameter, network structures, and the prey-taxis coefficient are shown to influence Turing patterns. Different parameter sets cause distinctive patterns, like spots and stripes, to emerge gradually. Our simulations demonstrate the effects of various network layouts, namely Lattice (LA), Barabasi-Albert (BA), and Watts-Strogatz (WS) networks, on the node density distribution and the time needed for patterns to stabilize. We also show how the internal dynamics of networks influence species distribution in their environments. These results offer crucial new understandings of the intricate dynamics of prey-predator interactions in ecological networks.