Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/28776
Title: Codimension-two bifurcations analysis and tracking control on a discrete epidemic model
Authors: Yi, N
Zhang, Q
Liu, P
Lin, Y 
Keywords: Chaos
Codimension-two bifurcations
Discrete epidemic model
Tracking control
Issue Date: 2011
Publisher: Springer Heidelberg
Source: Journal of Systems Science and Complexity, 2011, v. 24, no. 6, p. 1033-1056 How to cite?
Journal: Journal of Systems Science and Complexity 
Abstract: In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1:1 strong resonance, 1:2 strong resonance, 1:3 strong resonance and 1:4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.
URI: http://hdl.handle.net/10397/28776
DOI: 10.1007/s11424-011-9041-0
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