The dynamical behavior of the extended Duffing-Van der Pol oscillator is investigated numerically in detail. With the aid of some numerical simulation tools such as bifurcation diagrams and Poinearé maps, the dif...The dynamical behavior of the extended Duffing-Van der Pol oscillator is investigated numerically in detail. With the aid of some numerical simulation tools such as bifurcation diagrams and Poinearé maps, the different routes to chaos and various shapes of strange attractors are observed. To characterize chaotic behavior of this oscillator system, the spectrum of Lyapunov exponent and Lyapunov dimension are also employed.展开更多
This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of...This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10875078the Natural Science Foundation of Zhejiang Province of China under Grant No.Y7080455
文摘The dynamical behavior of the extended Duffing-Van der Pol oscillator is investigated numerically in detail. With the aid of some numerical simulation tools such as bifurcation diagrams and Poinearé maps, the different routes to chaos and various shapes of strange attractors are observed. To characterize chaotic behavior of this oscillator system, the spectrum of Lyapunov exponent and Lyapunov dimension are also employed.
文摘This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.
