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Instability induced by cross-diffusion in reaction–diffusion systems
Abstract In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions forExpand
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Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion
TLDR
This paper is concerned with the study of pattern formation for an inhomogeneous Brusselator model with cross-diffusion, modeling an autocatalytic chemical reaction taking place in a three-dimensional domain. Expand
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Existence and asymptotic behavior of solutions for quasilinear parabolic systems
This paper is concerned with the existence, uniqueness, and asymptotic behavior of solutions for the quasilinear parabolic systems with mixed quasimonotone reaction functions, the elliptic operatorsExpand
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Traveling wave solutions for delayed reaction-diffusion systems
This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iterationExpand
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Mathematical analysis and numerical simulation of pattern formation under cross-diffusion
a b s t r a c t Cross-diffusion driven instabilities have gained a considerable attention in the field of population dynamics, mainly due to their ability to predict some important features in theExpand
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Delay-driven spatial patterns in a plankton allelopathic system.
Spatial patterns have received considerable attention in the physical, biological, and social sciences. Generally speaking, time delay is a prevailing phenomenon in aquatic environments, since theExpand
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Turing pattern dynamics in an activator-inhibitor system with superdiffusion.
  • L. Zhang, Canrong Tian
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and…
  • 19 December 2014
The fractional operator is introduced to an activator-inhibitor system to describe species anomalous superdiffusion. The effects of the superdiffusive exponent on pattern formation and patternExpand
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Delay-driven irregular spatiotemporal patterns in a plankton system.
An inhomogeneous distribution of species density over physical space is a widely observed scenario in plankton systems. Understanding the mechanisms resulting in these spatial patterns is a centralExpand
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Turing pattern formation in a predator–prey–mutualist system
Abstract In this paper, we develop a theoretical framework about spatial patterns in a three-species predator–prey–mutualist system with cross-diffusion. We concentrate on three aspects of TuringExpand
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Turing patterns created by cross-diffusion for a Holling II and Leslie-Gower type three species food chain model
In this paper, we develop a theoretical framework for a research into spatial patterns in a three-species Holling II and Leslie-Gower type food chain model with cross-diffusion, the results of whichExpand
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