Stability of Traveling Wave Fronts for Delayed Lotka-Volterra Competition Systems With Stage Structures

GUO Zhihua; CAO Huarong

doi:10.21656/1000-0887.380293

Volume 39 Issue 9

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GUO Zhihua, CAO Huarong. Stability of Traveling Wave Fronts for Delayed Lotka-Volterra Competition Systems With Stage Structures[J]. Applied Mathematics and Mechanics, 2018, 39(9): 1051-1067. doi: 10.21656/1000-0887.380293

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Stability of Traveling Wave Fronts for Delayed Lotka-Volterra Competition Systems With Stage Structures

doi: 10.21656/1000-0887.380293

School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

Funds: The National Natural Science Foundation of China(11671315)

Received Date: 2017-11-22
Rev Recd Date: 2018-02-26
Publish Date: 2018-09-15

Abstract

Abstract

The stability of traveling wave solutions to a class of Lotka-Volterra competitive systems with age structures was studied. In the case of quasi-monotonicity, the existence and comparison theorems for the solutions to the initial value problems of the systems were first established on R with the analytic semigroup theory and the abstract functional differential equations. Then based on the weighted energy method, the comparison theorem as well as the embedding theorem, the global exponential stability of the monostable large-speed traveling wave solutions under the so-called large initial perturbation (i.e. the initial perturbation around the traveling wave decaying exponentially as x→-∞,but being arbitrarily large at other locations) was obtained for the systems in the weighted Sobolev space. The results show that, as the steady state solution of the system, the traveling wave solution usually determines the long-term asymptotic behavior of the solution to the initial value problem. Its stability reveals that the phenomena and results of inter-species competition systems can be clearly observed without interference by external factors.
- Lotka-Volterra competition model,
- stage structure,
- traveling wave solution,
- stability

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References(26)

References

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