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Nonlinear Dynamics

, Volume 63, Issue 4, pp 521–535 | Cite as

Bifurcation and chaos of biochemical reaction model with impulsive perturbations

  • Zhong Zhao
  • Li Yang
  • Lansun Chen
Original Paper

Abstract

In this paper, a biochemical model with the impulsive perturbations is considered. By using the Floquet theorem for the impulsive equation and small-amplitude perturbation skills, we see that the boundary-periodic solution \((\tilde{x}(t),0)\) is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. By numerical simulation, we can show that the system presents rich dynamics, including periodic solutions, quasi-periodic oscillations, period doubling cascades, periodic halving cascades, symmetry bifurcations, and chaos.

Keywords

Stability Nontrivial periodic solutions Strange attractor Bifurcation Chaos 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsHuanghuai UniversityZhumadianChina
  2. 2.Department of Applied MathematicsDalian University of TechnologyDalianChina

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