In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative i...In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.展开更多
In this paper, a 3D chaotic system with multi-parameters is introduced. The dynamical systems of the original ADVP circuit and the modified ADVP model are regarded as special examples to the system. Some basic dynamic...In this paper, a 3D chaotic system with multi-parameters is introduced. The dynamical systems of the original ADVP circuit and the modified ADVP model are regarded as special examples to the system. Some basic dynamical behaviors such as the stability of equilibria, the existence of Hopf bifurcation are investigated. We analyse the Hopf bifurcation of the system comprehensively using the first Lyapunov coefficient by precise symbolic computation. As a result, in fact we have studied the further dynamical behaviors.展开更多
Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplaci...Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplacian operators are obtained. Moreover, we construct an example to illustrate the feasibility of our results.展开更多
In this paper, a time fractional advection-dispersion equation is considered. From the relationship between the Caputo derivative and the Griinwald derivative, the Caputo derivative is approximated by using the Griinw...In this paper, a time fractional advection-dispersion equation is considered. From the relationship between the Caputo derivative and the Griinwald derivative, the Caputo derivative is approximated by using the Griinwald derivative. An implicit difference approximation for this equation is proposed. We prove that this approximation is unconditionally stable and convergent. Finally, numerical examples are given.展开更多
文摘In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.
基金the National Natural Science Foundation of China (No.10671105)
文摘In this paper, a 3D chaotic system with multi-parameters is introduced. The dynamical systems of the original ADVP circuit and the modified ADVP model are regarded as special examples to the system. Some basic dynamical behaviors such as the stability of equilibria, the existence of Hopf bifurcation are investigated. We analyse the Hopf bifurcation of the system comprehensively using the first Lyapunov coefficient by precise symbolic computation. As a result, in fact we have studied the further dynamical behaviors.
基金sponsored by the National Natural Science Foundation of China (11071001)NSF of Education Bureau of Anhui Province (KJ2009A005Z+2 种基金KJ2010ZD022010SQRL159)Anhui Provincial Natural Science Foundation (1208085MA13)
文摘Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplacian operators are obtained. Moreover, we construct an example to illustrate the feasibility of our results.
文摘In this paper, a time fractional advection-dispersion equation is considered. From the relationship between the Caputo derivative and the Griinwald derivative, the Caputo derivative is approximated by using the Griinwald derivative. An implicit difference approximation for this equation is proposed. We prove that this approximation is unconditionally stable and convergent. Finally, numerical examples are given.
