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排序方式: 共有124条查询结果,搜索用时 15 毫秒
71.
Estimating the Lyapunov exponents of discrete systems 总被引:1,自引:0,他引:1
In the present paper, our aim is to determine both upper and lower bounds for all the Lyapunov exponents of a given finite-dimensional discrete map. To show the efficiency of the proposed estimation method, two examples are given, including the well-known Henon map and a coupled map lattice. 相似文献
72.
Li Chunbiao Xu Yujie Chen Guanrong Liu Yongjian Zheng Jincun 《Nonlinear dynamics》2019,95(2):1245-1256
Nonlinear Dynamics - Coexisting attractors with conditional symmetry exist in separated asymmetric basins of attraction with identical Lyapunov exponents. It is found that when a periodic function... 相似文献
73.
74.
In this paper, a generalized epidemic model on complex heterogeneous networks is proposed. To give a theoretical explanation for the simulation results established on networks, mathematical analysis of the epidemic dynamics is presented via mean-field approximation. Stabilities of the disease-free equilibrium and the endemic equilibrium are studied. The results explain why the heterogeneous connectivity patterns impact the epidemic threshold and reveal how the host parameters and the underlying network structures determine disease propagation. 相似文献
75.
This paper investigates the impact of edge-adding number m and edge-adding distance d on both synchronizability and average path length of NW small-world networks generated from ring networks via random edge-adding. It is found that the synchronizability of the network as a function of the distance d is fluctuant and there exist some d that have almost no impact on the synchronizability and may only scarcely shorten the average path length of the network. Numerical simulations on a network of Lorenz oscillators confirm the above results. This phenomenon shows that the contributions of randomly added edges to both the synchronizability and the average path length are not uniform nor monotone in building an NW small-world network with equal-distance edge additions, implying that only if appropriately adding edges when building up the NW small-word network can help enhance the synchronizability and/or reduce the average path length of the resultant network. Finally, it is shown that this NW small-world network has worse synchronizability and longer average path length, when compared with the conventional NW small-world network, with random-distance edge additions. This may be due to the fact that with equal-distance edge additions, there is only one shortcut distance for better information exchange among nodes and for shortening the average path length, while with random-distance edge additions, there exist many different distances for doing so. 相似文献
76.
Guanghu Zhu Xinchu Fu Guanrong Chen 《Communications in Nonlinear Science & Numerical Simulation》2012,17(6):2588-2594
In this paper, a new epidemic SIS model with nonlinear infectivity, as well as birth and death of nodes and edges, is investigated on heterogeneous networks. The global behavior of the model is studied mathematically. When the basic reproductive number is less than or equal to unity, it is verified that the disease dies out; otherwise, the model solutions lead to positive steady states. This paper provides a concise mathematical analysis to verify the global dynamics of the model. 相似文献
77.
Simin Yu Guanrong Chen 《Communications in Nonlinear Science & Numerical Simulation》2012,17(6):2617-2627
Based on two basic characteristics of continuous-time autonomous chaotic systems, namely being globally bounded while having a positive Lyapunov exponent, this paper develops a universal and practical anti-control approach to design a general continuous-time autonomous chaotic system via Lyapunov exponent placement. This self-unified approach is verified by mathematical analysis and validated by several typical systems designs with simulations. Compared to the common trial-and-error methods, this approach is semi-analytical with feasible guidelines for design and implementation. Finally, using the Shilnikov criteria, it is proved that the new approach yields a heteroclinic orbit in a three-dimensional autonomous system, therefore the resulting system is indeed chaotic in the sense of Shilnikov. 相似文献
78.
On a four-dimensional chaotic system 总被引:12,自引:0,他引:12
Guoyuan Qi Shengzhi Du Guanrong Chen Zengqiang Chen Zhuzhi yuan 《Chaos, solitons, and fractals》2005,23(5):1671-1682
This paper reports a new four-dimensional continuous autonomous chaotic system, in which each equation in the system contains a 3-term cross product. Basic properties of the system are analyzed by means of Lyapunov exponents and bifurcation diagrams. 相似文献
79.
On the generalized Lorenz canonical form 总被引:7,自引:0,他引:7
This short note is to briefly introduce the new notion of generalized Lorenz canonical form (GLCF), which contains the classical Lorenz system and the newly discovered Chen system as two extreme cases, along with infinitely many chaotic systems in between. It also points out that some recently reported chaotic systems are special cases of the GLCF. 相似文献
80.
This paper considers the computation of the simplest parameterized normal forms (SPNF) of Hopf and generalized Hopf bifurcations.
Although the notion of the simplest normal form has been studied for more than two decades, most of the efforts have been
spent on the systems that do not involve perturbation parameters due to the restriction of the computational complexity. Very
recently, two singularities – single zero and Hopf bifurcation – have been investigated, and the SPNFs for these two cases
have been obtained. This paper extends a recently developed method for Hopf bifurcation to compute the SPNF of generalized
Hopf bifurcations. The attention is focused on a codimension-2 generalized Hopf bifurcation. It is shown that the SPNF cannot
be obtained by using only a near-identity transformation. Additional transformations such as time and parameter rescaling
are further introduced. Moreover, an efficient recursive formula is presented for computing the SPNF. Examples are given to
demonstrate the applicability of the new method. 相似文献