Extinction and Permanence of a Three‐Species Lotka‐Volterra System with Impulsive Control Strategies | Zendy

Hunki Baek | Zendy

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Extinction and Permanence of a Three‐Species Lotka‐Volterra System with Impulsive Control Strategies

Author(s) -

Hunki Baek

Publication year - 2008

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2008/752403

Subject(s) - floquet theory , impulse (physics) , control theory (sociology) , mathematics , perturbation (astronomy) , differential equation , chaotic , impulse control , comparison theorem , amplitude , mathematical analysis , physics , nonlinear system , control (management) , computer science , classical mechanics , biology , quantum mechanics , artificial intelligence , neuroscience

A three-species Lotka-Volterra system with impulsive control strategies containingthe biological control (the constant impulse) and the chemical control (the proportionalimpulse) with the same period, but not simultaneously, is investigated. Byapplying the Floquet theory of impulsive differential equation and small amplitudeperturbation techniques to the system, we find conditions for local and global stabilitiesof a lower-level prey and top-predator free periodic solution of the system. Inaddition, it is shown that the system is permanent under some conditions by usingcomparison results of impulsive differential inequalities. We also give a numericalexample that seems to indicate the existence of chaotic behavior

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