Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We fi...Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.展开更多
To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coup...To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.展开更多
In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biol...In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz （1963） model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures （sensitivity functions） to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.展开更多
文摘Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.
基金Projects(61073187,61161006) supported by the National Nature Science Foundation of ChinaProject supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry,China
文摘To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
文摘In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz （1963） model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures （sensitivity functions） to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.
