Uniform Persistence, Coexistence, and Extinction in Almost Periodic/Nonautonomous Competition Diffusion Systems

2002 ◽  
Vol 34 (1) ◽  
pp. 204-227 ◽  
Author(s):  
Georg Hetzer ◽  
Wenxian Shen
Keyword(s):  
Uniform Persistence ◽  
Almost Periodic ◽  
Diffusion Systems ◽  
Competition Diffusion

scholarly journals Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hui Zhou ◽  
Jehad Alzabut ◽  
Shahram Rezapour ◽  
Mohammad Esmael Samei
Keyword(s):  
Differential Inequality ◽  
Almost Periodic Solution ◽  
Rocky Intertidal ◽  
Uniform Persistence ◽  
Almost Periodic ◽  
Patch Occupancy ◽  
Sharp Threshold ◽  
Intertidal Community ◽  
Patch Occupancy Model ◽  
Inequality Techniques

Abstract In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes.

Asymptotic spreading of competition diffusion systems: The role of interspecific competitions

2012 ◽  
Vol 23 (6) ◽  
pp. 669-689 ◽  
Author(s):  
GUO LIN ◽  
WAN-TONG LI
Keyword(s):  
Comparison Principle ◽  
Population Densities ◽  
Competitive Systems ◽  
Diffusion Systems ◽  
Negative Role ◽  
Asymptotic Spreading ◽  
Competition Diffusion

This paper is concerned with the asymptotic spreading of competition diffusion systems, with the purpose of formulating the propagation modes of a co-invasion–coexistence process of two competitors. Using the comparison principle for competitive systems, some results on asymptotic spreading are obtained. Our conclusions imply that the interspecific competitions slow the invasion of one species and decrease the population densities in the coexistence domain. Therefore, the interspecific competitions play a negative role in the evolution of competitive communities.

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