Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of fractional Bernstein bases. Moreover, some basic properties were dicussed and a theo...Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of fractional Bernstein bases. Moreover, some basic properties were dicussed and a theorem connected to Poisson curves was obtained. Some examples in this paper were given by the visual results.展开更多
This paper proposes three fractional discrete chaotic systems based on the Rulkov,Chang,and Zeraoulia–Sprott rational maps.The dynamics of the proposed maps are investigated by means of phase plots and bifurcations d...This paper proposes three fractional discrete chaotic systems based on the Rulkov,Chang,and Zeraoulia–Sprott rational maps.The dynamics of the proposed maps are investigated by means of phase plots and bifurcations diagrams.Adaptive stabilization schemes are proposed for each of the three maps and the convergence of the states is established by using the Lyapunov method.Furthermore,a combination synchronization scheme is proposed whereby a combination of the fractional Rulkov and Chang maps is synchronized to the fractional Zeraoulia-Sprott map.Numerical results are used to confirm the findings of the paper.展开更多
In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m s...In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.展开更多
文摘Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of fractional Bernstein bases. Moreover, some basic properties were dicussed and a theorem connected to Poisson curves was obtained. Some examples in this paper were given by the visual results.
基金supported by the Natural Science Foundation of China under Grant Nos.11726624,11726623,61473237the Natural Science Basic Research Plan in Shaxanxi Province of China under Grant No.2018GY-091the Natural Science Basic Research Plan in Shandong Province of China under Grant No.ZR2017PA008。
文摘This paper proposes three fractional discrete chaotic systems based on the Rulkov,Chang,and Zeraoulia–Sprott rational maps.The dynamics of the proposed maps are investigated by means of phase plots and bifurcations diagrams.Adaptive stabilization schemes are proposed for each of the three maps and the convergence of the states is established by using the Lyapunov method.Furthermore,a combination synchronization scheme is proposed whereby a combination of the fractional Rulkov and Chang maps is synchronized to the fractional Zeraoulia-Sprott map.Numerical results are used to confirm the findings of the paper.
文摘In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.
