This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide...This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.展开更多
This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system struct...This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.展开更多
When dynamic behaviors of temporal chaotic system are analyzed, we find that a temporal chaotic system has not only generic dynamic behaviors of chaotic reflection, but also has phenomena influencing two chaotic attra...When dynamic behaviors of temporal chaotic system are analyzed, we find that a temporal chaotic system has not only generic dynamic behaviors of chaotic reflection, but also has phenomena influencing two chaotic attractors by original values. Along with the system parameters changing to certain value, the system will appear a break in chaotic region, and jump to another orbit of attractors. When it is opposite that the system parameters change direction, the temporal chaotic system appears complicated chaotic behaviors.展开更多
In recent years,there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle,butterfly,heart and apple.This paper describes a new 3-D chaotic dynamical system with...In recent years,there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle,butterfly,heart and apple.This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve.The proposed chaotic system has two quadratic,two cubic and two quartic nonlinear terms.It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points.It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states.A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve.We have shown MATLAB plots to illustrate the capsule equilibrium curve,phase orbits of the new chaotic system,bifurcation diagrams and multi-stability.As an engineering application,we have proposed a speech cryptosystem with a numerical algorithm,which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve.The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array(FPGA)platform.Experimental results show that the proposed encryption system utilizes 33%of the FPGA,while the maximum clock frequency is 178.28 MHz.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin,China (Grant Nos 07JCZDJC09600,08JCZDJC21900 and 08JCZDJC18600)the Tianjin Key Laboratory for Control Theory & Applications in Complicated Industry Systems of China
文摘This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.
基金This research was supported by the National Natural Science Foundation of China under Grant No.60641006.
文摘This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.
文摘When dynamic behaviors of temporal chaotic system are analyzed, we find that a temporal chaotic system has not only generic dynamic behaviors of chaotic reflection, but also has phenomena influencing two chaotic attractors by original values. Along with the system parameters changing to certain value, the system will appear a break in chaotic region, and jump to another orbit of attractors. When it is opposite that the system parameters change direction, the temporal chaotic system appears complicated chaotic behaviors.
基金funded by the Center for Research Excellence,Incubation Management Center,Universiti Sultan Zainal Abidin via an internal grant UniSZA/2021/SRGSIC/07.
文摘In recent years,there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle,butterfly,heart and apple.This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve.The proposed chaotic system has two quadratic,two cubic and two quartic nonlinear terms.It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points.It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states.A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve.We have shown MATLAB plots to illustrate the capsule equilibrium curve,phase orbits of the new chaotic system,bifurcation diagrams and multi-stability.As an engineering application,we have proposed a speech cryptosystem with a numerical algorithm,which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve.The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array(FPGA)platform.Experimental results show that the proposed encryption system utilizes 33%of the FPGA,while the maximum clock frequency is 178.28 MHz.
