In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This k...In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.展开更多
In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a ...In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a semiconductor laser. This type of global bifurcation can be considered as a stylized mathematical description of self-pulsation in this laser type, associ-ated with saturation. The location is achieved by use of a custom algorithm based on the method of orthogonal collocation on finite elements with fourth order boundary conditions, constructed through scale order approximations. The effectiveness of the algorithm and the superiority of high-order boundary conditions over the widely used first order ones are justified throughout the obtained graphical results.展开更多
文摘In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.
文摘In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a semiconductor laser. This type of global bifurcation can be considered as a stylized mathematical description of self-pulsation in this laser type, associ-ated with saturation. The location is achieved by use of a custom algorithm based on the method of orthogonal collocation on finite elements with fourth order boundary conditions, constructed through scale order approximations. The effectiveness of the algorithm and the superiority of high-order boundary conditions over the widely used first order ones are justified throughout the obtained graphical results.
