A In this paper, we employ both bifurcation method of dynamical systems and numerical exploration of differential equations to investigate the periodic waves of a general compressible hyperelastic rod equation ut＋3uu...A In this paper, we employ both bifurcation method of dynamical systems and numerical exploration of differential equations to investigate the periodic waves of a general compressible hyperelastic rod equation ut＋3uux-uxxt-γ（2uxuxx＋uuxxx）=0, with parameter γ 〈 0. New expressions including explicit expressions and implicit expressions are obtained. Some previous results are extended. Specially, a new phenomenon is found： when the initial value tends to a certain number, the periodic shock wave suddenly changes into a smooth periodic wave. In dynamical systems, this represents that one of orbits can pass through the singular line. The coherency of numerical simulation and theoretical derivation implies the correctness of our results.展开更多
Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical exploration.The investigation is based on detection functions which are partic...Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical exploration.The investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian system.The study reveals that the system has 3 limit cycles.By the method of numerical simulation,the distributed orderliness of the 3 limitcycles is observed,and their nicety places are determined.The study also indicates that each of the 3 limit cycles passes the corresponding nicety point.展开更多
基金Research is supported by the National Natural Science Foundation of China （No.10571062）.
文摘A In this paper, we employ both bifurcation method of dynamical systems and numerical exploration of differential equations to investigate the periodic waves of a general compressible hyperelastic rod equation ut＋3uux-uxxt-γ（2uxuxx＋uuxxx）=0, with parameter γ 〈 0. New expressions including explicit expressions and implicit expressions are obtained. Some previous results are extended. Specially, a new phenomenon is found： when the initial value tends to a certain number, the periodic shock wave suddenly changes into a smooth periodic wave. In dynamical systems, this represents that one of orbits can pass through the singular line. The coherency of numerical simulation and theoretical derivation implies the correctness of our results.
基金supported by the Natural Science Foundation of China(Grant No.11161038)
文摘Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical exploration.The investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian system.The study reveals that the system has 3 limit cycles.By the method of numerical simulation,the distributed orderliness of the 3 limitcycles is observed,and their nicety places are determined.The study also indicates that each of the 3 limit cycles passes the corresponding nicety point.
