Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained ...Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.展开更多
Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript.With the Me...Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript.With the Melnikov method,the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically.The feature of the critical curves separating chaotic and non-chaotic regions on the excitation frequency and the time delay is investigated analytically in detail.The monotonicity of the critical value to the excitation frequency and time delay is obtained rigorously.It is presented that there may exist a special frequency for this system.With this frequency,chaos in the sense of Melnikov may not occur for any excitation amplitudes.There also exists a uncontrollable time delay with which chaos always occurs for this system.Numerical simulations are carried out to verify the chaos threshold obtained by the analytical method.展开更多
基金supported by the National Natural Science Foundation of China(11172125,11202095 and 11201226)Natural Science Foundation of Henan,China(2009B110009,B2008-56 and 649106)
文摘Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.
基金supported by the National Natural Science Foundation of China(No.11772148,12172166 and 11872201)China Postdoctoral Science Foundation(No.2013T60531)。
文摘Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript.With the Melnikov method,the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically.The feature of the critical curves separating chaotic and non-chaotic regions on the excitation frequency and the time delay is investigated analytically in detail.The monotonicity of the critical value to the excitation frequency and time delay is obtained rigorously.It is presented that there may exist a special frequency for this system.With this frequency,chaos in the sense of Melnikov may not occur for any excitation amplitudes.There also exists a uncontrollable time delay with which chaos always occurs for this system.Numerical simulations are carried out to verify the chaos threshold obtained by the analytical method.
