Spreading speeds and linear determinacy of time dependent diffusive cooperative/competitive systems
type: Item
instance of: scholarly article
title: Spreading speeds and linear determinacy of time dependent diffusive cooperative/competitive systems
zbMATH Open document ID: 1395.35011
author: Wenxian Shen
author: Zhi-Cheng Wang
author: Xiongxiong Bao
author: Wan-Tong Li
published in: Journal of Differential Equations
publication date: 2018-06-18T00:00:00Z
review text: This is a study of spreading speeds and linear determinacy of diffusive either cooperative or competitive systems of the form \(u_t(t,x)=(Au)(t,x)+F(t,u(t,x))\) either in \({\mathbb R}^N\) or on the lattice \({\mathbb Z}^N\). Here \(A\) is a random or nonlocal dispersal operator, or a discrete dispersal operator. The nonlinearity \(F(t, u)\) is cooperative or competitive in \(u\) and is recurrent in time, e.g. \(F(t u)\) periodic and almost periodic in \(t\) as special cases. The notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds. Then, some principal Lyapunov exponent and principal Floquet bundle theory for linear cooperative systems of ordinary differential equations is developed. These are the tools used in the proof that a diffusive cooperative system has a single spreading speed and is linearly determinant. Finally, by transforming a diffusive competitive system to a diffusive cooperative system and applying previous results, upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6890651
zbMATH Keywords: time recurrence
zbMATH Keywords: principal Lyapunov exponent
zbMATH Keywords: principal Floquet bundle
MaRDI profile type: Publication
full work available at URL: j.jde.2018.05.003
OpenAlex ID: W2802780478
cites work: Multidimensional nonlinear diffusion arising in population genetics
cites work: Traveling wave solutions of Lotka-Volterra competition systems with nonlocal dispersal in periodic habitats
cites work: The speed of propagation for KPP type problems. I: Periodic framework
cites work: The speed of propagation for KPP type problems. II: General domains
cites work: Spreading speeds and travelling waves in a delayed population model with stage structure on a 2D spatial lattice
cites work: Propagation speed of travelling fronts in non local reaction-diffusion equations
cites work: On a non-local equation arising in population dynamics
cites work: Principal Eigenvalues of Generalized Convolution Operators on the Circle and Spreading Speeds of Noncompact Evolution Systems in Periodic Media
cites work: Traveling Waves for Monotone Semiflows with Weak Compactness
cites work: Traveling waves and spreading speeds for time-space periodic monotone systems
cites work: The approach of solutions of nonlinear diffusion equations to travelling front solutions
cites work: Q4650438
cites work: Front propagation for discrete periodic monostable equations
cites work: Front propagation for a two-dimensional periodic monostable lattice dynamical system
cites work: The minimal speed of traveling fronts for the Lotka-Volterra competition system
cites work: Geometric theory of semilinear parabolic equations
cites work: Q3998030
cites work: The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model.
cites work: The evolution of dispersal
cites work: Speeds of Spread and Propagation for KPP Models in Time Almost and Space Periodic Media
cites work: Spreading speeds and traveling wave solutions in cooperative integral-differential systems
cites work: Ergodic Properties of Linear Dynamical Systems
cites work: Random dispersal vs. non-local dispersal
cites work: Spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in periodic habitats
cites work: Liouville type property and spreading speeds of KPP equations in periodic media with localized spatial inhomogeneity
cites work: Spreading speed and linear determinacy for two-species competition models
cites work: Spreading speeds as slowest wave speeds for cooperative systems
cites work: Invasion entire solutions in a competition system with nonlocal dispersal
cites work: Asymptotic speeds of spread and traveling waves for monotone semiflows with applications
cites work: Spreading speeds and traveling waves for periodic evolution systems
cites work: Biological growth and spread modeled by systems of recursions. I: Mathematical theory
cites work: Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I: General theory
cites work: Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems
cites work: Q5459964
cites work: Propagation phenomena for time heterogeneous KPP reaction-diffusion equations
cites work: Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds
cites work: Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications
cites work: Spreading speeds and traveling waves of nonlocal monostable equations in time and space periodic habitats
cites work: Q5613838
cites work: Spreading and generalized propagating speeds of discrete KPP models in time varying environments
cites work: Variational principle for spreading speeds and generalized propagating speeds in time almost periodic and space periodic KPP models
cites work: Existence, uniqueness, and stability of generalized traveling waves in time dependent monostable equations
cites work: Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats
cites work: Almost automorphic and almost periodic dynamics in skew-product semiflows
cites work: Entire solutions in nonlocal dispersal equations with bistable nonlinearity
cites work: Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction--diffusion models.
cites work: Entire Solutions in Delayed Lattice Differential Equations with Monostable Nonlinearity
cites work: Analysis of linear determinacy for spread in cooperative models
cites work: Long-Time Behavior of a Class of Biological Models
cites work: On spreading speeds and traveling waves for growth and migration models in a periodic habitat
cites work: Propagation phenomena for A reaction-advection-diffusion competition model in a periodic habitat
Wikidata QID: Q129871640
DOI: 10.1016/J.JDE.2018.05.003