The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Me...The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones.展开更多
With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GB...With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GBK） system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.展开更多
Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are train...Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua＇s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.展开更多
With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal loca...With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.展开更多
In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the d...In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the differential equations, the natural frequencies are estimated by neglecting the coupling between tangential and normal direction. By use of numerical integration method, solutions are obtained. On this basis, strange attractors and bifurcation phenomena are obtained by applying Poineare map, phase plots and bifurcation diagram, showing the existence of the chaotic response in this system when wave steepness is high enough.展开更多
文摘The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant Nos. Y6100257,Y6090545,and Y6110140)the Scientific Research Fund of Zhejiang Provincial Education Department,China (Grant No. Z201120169)
文摘With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GBK） system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61072103)the Jiangxi Province Training Program for Younger Scientists
文摘Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua＇s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106, Y606128the Scientific Research Fund of Zhejiang Provincial Education Department of China under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KY08003
文摘With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.
基金supported by the Key Program of National Natural Science Foundation of China (Grant No.50739004) the Shandong Province Key Lab of Ocean Engineering in Ocean University of China
文摘In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the differential equations, the natural frequencies are estimated by neglecting the coupling between tangential and normal direction. By use of numerical integration method, solutions are obtained. On this basis, strange attractors and bifurcation phenomena are obtained by applying Poineare map, phase plots and bifurcation diagram, showing the existence of the chaotic response in this system when wave steepness is high enough.
