This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system...This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.展开更多
In this paper, the generation of striped trajectories in phase space by noise-injection is considered. With suitable amplitudes of noise, the steady-state system orbits appear in rectangular striped shape. The relatio...In this paper, the generation of striped trajectories in phase space by noise-injection is considered. With suitable amplitudes of noise, the steady-state system orbits appear in rectangular striped shape. The relationship between the shape （including the range and the number of stripes） and some parameters is discussed. The result shows that noise can also generate the striped shape effectively and simply, which is similar to the newly-discovered striped pattern generated by controlled Rossler systems.展开更多
Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to ...Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.展开更多
This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler l...This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.展开更多
This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which...This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronizution law. The proposed impulsive control scheme is illustrated by nonlinear Rossler chaotic systems and the simulation results demonstrate the effectiveness of the method.展开更多
The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies,...The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies, but seldom is it used to treat the au-tonomous systems and cases without motion equations. Based on one-dimensional maps,展开更多
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a...Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.展开更多
A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability ...A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.展开更多
基金Project supported by the Key Youth Project of Southwest University for Nationalities of China and the Natural Science Foundation of the State Nationalities Affairs Commission of China （Grant Nos 05XN07 and 07XN05）.
文摘This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.
文摘In this paper, the generation of striped trajectories in phase space by noise-injection is considered. With suitable amplitudes of noise, the steady-state system orbits appear in rectangular striped shape. The relationship between the shape （including the range and the number of stripes） and some parameters is discussed. The result shows that noise can also generate the striped shape effectively and simply, which is similar to the newly-discovered striped pattern generated by controlled Rossler systems.
文摘Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.
文摘This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.
基金Project supported by the Major Program of the National Natural Science Foundation of China （Grant No 60271019）, the Doctorate Foundation of the Ministry of Education of China （Grant No 20020611007）.
文摘This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronizution law. The proposed impulsive control scheme is illustrated by nonlinear Rossler chaotic systems and the simulation results demonstrate the effectiveness of the method.
基金Project supported by the National Basic Research Project"Nonlinear Science"of Chinathe National Natural Science Foundation of China
文摘The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies, but seldom is it used to treat the au-tonomous systems and cases without motion equations. Based on one-dimensional maps,
文摘Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.
基金Project supported by the National Natural Science Foundation of China （Grant No 20373021） and Natural Science Foundation of Liaoning Province （Grant No 20052151）.
文摘A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.
