In this paper,we consider the first-order Melnikov functions and limit cycle bifurcations of a nearHamiltonian system near a cuspidal loop.By establishing relations between the coefficients in the expansions of the tw...In this paper,we consider the first-order Melnikov functions and limit cycle bifurcations of a nearHamiltonian system near a cuspidal loop.By establishing relations between the coefficients in the expansions of the two Melnikov functions,we give a general method to obtain the number of limit cycles near the cuspidal loop.As an application,we consider a kind of Liénard systems and obtain a new estimation on the lower bound of the maximum number of limit cycles.展开更多
Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the s...Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincar6 map. The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation. While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences, and bring about two antisymmetric chaotic attractors subse- quently. If the symmetric system is transformed into asymmetric one, bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.展开更多
Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for...Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture vas established, and a critical condition associated with the model is given.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11971145)supported by National Natural Science Foundation of China(Grant No.11931016)the National Key R&D Program of China(Grant No.2022YFA1005900)。
文摘In this paper,we consider the first-order Melnikov functions and limit cycle bifurcations of a nearHamiltonian system near a cuspidal loop.By establishing relations between the coefficients in the expansions of the two Melnikov functions,we give a general method to obtain the number of limit cycles near the cuspidal loop.As an application,we consider a kind of Liénard systems and obtain a new estimation on the lower bound of the maximum number of limit cycles.
基金Project supported by the National Natural Science Foundation of China (No.10472096)the Fund for Doctoral Innovation of Southwest Jiaotong University
文摘Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincar6 map. The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation. While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences, and bring about two antisymmetric chaotic attractors subse- quently. If the symmetric system is transformed into asymmetric one, bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.
文摘Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture vas established, and a critical condition associated with the model is given.
