Global Existence, Uniqueness and Pathwise Property of Solutions to a Stochastic Rossler-Lorentz System

The authors integrate two well-known systems, the Rossler and Lorentz systems, to introduce a new chaotic system, called the Lorentz-Rossler system. Then, taking into account the effect of environmental noise, the authors incorporate white noise in both Rossler and Lorentz systems to have a corresponding stochastic system. By deriving the uniform a priori estimates for an approximate system and then taking them to the limit, the authors prove the global existence, uniqueness and the pathwise property of solutions to the Lorentz-Rossler system. Moreover, the authors carried out a number of numerical experiments, and the numerical results demonstrate their theoretic analysis and show some new qualitative properties of solutions which reveal that the Lorentz-Rossler system could be used to design more complex and more secure nonlinear hop-frequence time series.