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- Title
An upper bound for the amplitude of limit cycles of Liénard-type differential systems.
- Authors
Fangfang Jiang; Zhicheng Ji; Yan Wang
- Abstract
In this paper, we investigate the position problem of limit cycles for a class of Liénard-type differential systems. By considering the upper bound of the amplitude of limit cycles on {(x, y) ∈ ℝ² : x < 0} and {(x, y) ∈ ℝ² : x > 0} respectively, we provide a criterion concerning an explicit upper bound for the amplitude of the unique limit cycle of the Liénard-type system on the plane. Here the amplitude of a limit cycle on {(x, y) ∈ ∈ : x < 0} (resp. {(x, y) ∈ ∈ : x > 0}) is defined as the minimum (resp. maximum) value of the x-coordinate on such a limit cycle. Finally, we give two examples including an application to predator-prey system model to illustrate the obtained theoretical result, and Matlab simulations are presented to show the agreement between our theoretical result with the simulation analysis.
- Subjects
EXTERIOR differential systems; LIMIT cycles; LOTKA-Volterra equations; SIMULATION methods &; models; DIFFERENTIAL equations
- Publication
Electronic Journal of Qualitative Theory of Differential Equations, 2017, Issue 25-44, p1
- ISSN
1417-3875
- Publication type
Article
- DOI
10.14232/ejqtde.2017.1.34