![]() A robust Gauss-Seidel like implicit finite-difference method (GS1) has been developed and used for the solution of the resulting initial-value problem (IVP). The quasi-periodic motion is stable for a small parameter region. It is interesting to note that in the vicinity of the double-Hopf compound critical point, there exist periodic as well as quasi-periodic solutions. Furthermore, bifurcation analysis reveals that the limit cycles associated with the first Brusselator are always stable, while that generated by the second Brusselator may be unstable if the parameter values are chosen far from the stability boundary. The motion of the oscillator may either be periodic (bifurcating from a Hopf-type critical point), or quasi-periodic (bifurcating from a compound critical point). Of particular interest is the study of the associated Hopf bifurcation and double-Hopf bifurcations. Moreover, it is more economical computationally.Ībstract = "This paper addresses the dynamic behaviour of a chemical oscillator arising from the series coupling of two Brusselators. Unlike the RK4, which fails when large time steps are used to integrate the IVP, extensive numerical simulations with appropriate initial data suggest that the GS1 method is unconditionally convergent. In addition to being of comparable accuracy (judging by the similarity of the profiles generated) with the fourth order Runge-Kutta method (RK4), the GS1 method will be seen to have better numerical stability property than RK4. ![]() These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.This paper addresses the dynamic behaviour of a chemical oscillator arising from the series coupling of two Brusselators. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.ĪB - In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. N2 - In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. © 2020 World Scientific Publishing Company. 14YZ114), and the Natural Sciences and Engineering Research Council of Canada (No. 11201294), the Innovation Program of Shanghai Municipal Education Commission (No. ![]() This research was partially supported by the National Natural Science Foundation of China (No. 11201294), the Innovation Program of Shanghai T1 - Tristable Phenomenon in a Predator-Prey System Arising from Multiple Limit Cycles Bifurcation
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