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MARIA CARMELA LOMBARDO

Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system

  • Autori: Gambino, G.; Lombardo, M.; Sammartino, M.
  • Anno di pubblicazione: 2008
  • Tipologia: Proceedings (TIPOLOGIA NON ATTIVA)
  • Parole Chiave: Nonlinear diffusion; Turing pattern formation
  • OA Link: http://hdl.handle.net/10447/39995

Abstract

In this work we investigate the possibility of the pattern formation for a reaction-di®usion system with nonlinear di®usion terms. Through a linear sta- bility analysis we ¯nd the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-di®usion e®ects are responsible for the initiation of spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.