Global dynamics and complex patterns in Lotka-Volterra systems: The effects of both local and nonlocal intraspecific and interspecific competitions

Xianyong Chen, Weihua Jiang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a Lotka-Volterra system with both local and nonlocal intraspecific and interspecific competitions, where nonlocal competitions depend on both spatial and temporal effects in a general form. Firstly, global stability of two constant semi-trivial equilibria and global convergence of the coexistence equilibrium are derived by using the functional and energy method, which implies that strengths of nonlocal intraspecific competitions have great effects on these global dynamics but the nonlocal interspecific competitions not and extends global results of Gourley and Ruan (2003) [11]. Secondly, global attracting region of each constant semi-trivial equilibrium is limited by its environment capacity regardless of the distinction of local and nonlocal intraspecific competitions. Thirdly, in the weak competition case, the coexistence equilibrium becomes Turing unstable when the kernels are chosen as generally distributed delay functions in temporal and the nonlocal intraspecific competitions are suitably strong. Additionally, spatially homogeneous and inhomogeneous periodic solutions are found numerically.

Original languageEnglish (US)
Article number125015
JournalJournal of Mathematical Analysis and Applications
Volume499
Issue number1
DOIs
StatePublished - Jul 1 2021

Keywords

  • Competitive Lotka-Volterra system
  • Global dynamics
  • Nonlocal intraspecific and interspecific competition
  • Turing instability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Global dynamics and complex patterns in Lotka-Volterra systems: The effects of both local and nonlocal intraspecific and interspecific competitions'. Together they form a unique fingerprint.

Cite this