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STRANGE ATTRACTORS IN SYMMETRIC UNFOLDINGS OF A SINGULARITY WITH THREE-FOLD ZERO EIGENVALUE
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作者 Qinghua Zhou (College of Mathematics and Information Sciences,Zhaoqing University,Zhaoqing 526061,Guangdong) 《Annals of Differential Equations》 2009年第2期228-238,共11页
In this paper,we study the Sil’nikov heteroclinic bifurcations,which display strange attractors,for the symmetric versal unfoldings of the singularity at the origin with a nilpotent linear part and 3-jet,using the no... In this paper,we study the Sil’nikov heteroclinic bifurcations,which display strange attractors,for the symmetric versal unfoldings of the singularity at the origin with a nilpotent linear part and 3-jet,using the normal form,the blow-up and the generalized Mel’nikov methods of heteroclinic orbits to two hyperbolic or nonhyperbolic equilibria in a high-dimensional space. 展开更多
关键词 SINGULARITY symmetric unfolding heteroclinic orbit sil'nikov bifur-cation strange attractor normal form BLOW-UP generalized Mel'nikov methods
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NONLINEAR VIBRATION RESPONSE AND BIFURCATION OF CIRCULAR CYLINDRICAL SHELLS UNDER TRAVELING CONCENTRATED HARMONIC EXCITATION 被引量:1
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作者 Yanqing Wang Li Liang +3 位作者 Xinghui Guo Jian Li Jing Liu Panglun Liu 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2013年第3期277-291,共15页
The nonlinear vibration of a cantilever cylindrical shell under a concentrated har- monic excitation moving in a concentric circular path is proposed. Nonlinearities due to large- amplitude shell motion are considered... The nonlinear vibration of a cantilever cylindrical shell under a concentrated har- monic excitation moving in a concentric circular path is proposed. Nonlinearities due to large- amplitude shell motion are considered, with account taken of the effect of viscous structure damp- ing. The system is discretized by Galerkin's method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifur- cation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations. 展开更多
关键词 circular cylindrical shell NONLINEARITY traveling wave method of averaging bifur-cation
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Effect of multiple delays on the dynamics of cannibalistic prey-predator system with disease in both populations
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作者 Santosh Biswas Sudip Samanta +1 位作者 Qamar J. A. Khan Joydev Chattopadhyayt 《International Journal of Biomathematics》 2017年第4期77-122,共46页
In the present paper, we investigate a prey-predator system with disease in both prey and predator populations and the predator population is cannibalistic in nature. The model is extended by introducing incubation de... In the present paper, we investigate a prey-predator system with disease in both prey and predator populations and the predator population is cannibalistic in nature. The model is extended by introducing incubation delays in disease transmission terms. Local stability analysis of the system around the biologically feasible equilibria is studied, The bifurcation analysis of the system around the interior equilibrium is also studied, The sufficient conditions for the permanence of the system are derived in the presence of delays. We observe that incubation delays have the ability to destabilize the cannibalistic prey-predator system. Finally, we perform numerical experiments to substantiate our analytical findings. 展开更多
关键词 CANNIBALISM disease transmission incubation delay PERSISTENCE Hopf bifur-cation.
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BIFURCATION AND SPATIOTEMPORAL PATTERNS IN A HOMOGENEOUS DIFFUSION-COMPETITION SYSTEM WITH DELAYS
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作者 JIA-FANG ZHANG WAN-TONG LI XIANG-PING YAN 《International Journal of Biomathematics》 2012年第6期19-41,共23页
A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotic... A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies com petition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters (delays) in the system cross some critical val ues. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifur cation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics. 展开更多
关键词 LotKa-Volterra competition system time delay spatial diffusion Hopf bifur-cation periodic solution.
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