Based on the property of solutions of the nonlinear differential equation,this paper focuses on the behavior of solutions to the two-dimensional Ikeda model,especially the dependence of the solutions on the parameter....Based on the property of solutions of the nonlinear differential equation,this paper focuses on the behavior of solutions to the two-dimensional Ikeda model,especially the dependence of the solutions on the parameter.The dependency relationship of the two-dimensional Ikeda model on the parameter is revealed by a large sample of proper numerical simulations.With the parameter varying from 0 to 1,the numerical solutions change from a point attractor to periodic solutions,then to chaos,and end up with a limit cycle.Furthermore,the route from bifurcation to chaos is shown to be continuous period-doubling bifurcations.The nonlinear structures presented by the solution of the two-dimensional Ikeda model indicate that,by setting different model parameters,one can test a new method that will be adopted to study atmospheric or oceanic predictability and/or stability.The corresponding test results provide some useful information on the ability of the new approach overcoming the impacts of strong nonlinearity.展开更多
By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in con...By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.展开更多
基金supported by the National Natural Science Foundation of China[grant number 41331174]
文摘Based on the property of solutions of the nonlinear differential equation,this paper focuses on the behavior of solutions to the two-dimensional Ikeda model,especially the dependence of the solutions on the parameter.The dependency relationship of the two-dimensional Ikeda model on the parameter is revealed by a large sample of proper numerical simulations.With the parameter varying from 0 to 1,the numerical solutions change from a point attractor to periodic solutions,then to chaos,and end up with a limit cycle.Furthermore,the route from bifurcation to chaos is shown to be continuous period-doubling bifurcations.The nonlinear structures presented by the solution of the two-dimensional Ikeda model indicate that,by setting different model parameters,one can test a new method that will be adopted to study atmospheric or oceanic predictability and/or stability.The corresponding test results provide some useful information on the ability of the new approach overcoming the impacts of strong nonlinearity.
基金Project supported by the National Natural Science Foundation of China (Grant No 10775060)in part by Doctoral Education Foundation of the Education Department of China and the Natural Science Foundation of Gansu Province
文摘By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.
