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[01463] Chemical Signalling and Pattern Formation in Predator-Prey Models

  • Session Time & Room : 4C (Aug.24, 13:20-15:00) @A601
  • Type : Contributed Talk
  • Abstract : Random movement of species is well documented to put forward Turing instability in predator-prey models . On the other hand recent studies suggest that directed movement of species known as direct taxis leads to stabilization of steady state and no patterns emerge. However the importance of chemical cues in predator-prey interactions is still a topic of contention among ecologists. Source of chemicals to which prey species respond often originate as cues released by the predators which lead to directed movement of prey individuals opposite to the concentration of chemicals. This movement of prey individuals opposite to the gradient of chemical is known as indirect predator taxis. This talk will introduce an advection-reaction-diffusion mathematical model to understand the impact of chemical induced anti-predation defense in a special class of predator-prey system. The reaction part considers Schoener's model of intraguild-predation which has no periodic solution. We will discuss uniqueness and existence of classical solutions, linear stability analysis results and conditions for the pattern formation. We will show that random diffusion forces constant steady state to be stable and only directed movement of prey individuals has ability to destabilizes the constant steady state and spatio-temporal patterns emerge. We numerically show emergence of spatio-temporal patterning that depicts the tendency to spatio-temporal separation between prey and predators.
  • Classification : 92B05, Mathematical Biology, Partial Differential Equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Purnedu Mishra (Norwegian University of Life Sciences Norway)
    • Prof. Darius Wrzosek (Norwegian University of Life Sciences)