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| Global Existence, Uniqueness and Pathwise Property ofSolutions to a Stochastic Rossler-Lorentz System |
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Citation： |
Song JIANG,Junping YIN.Global Existence, Uniqueness and Pathwise Property ofSolutions to a Stochastic Rossler-Lorentz System[J].Chinese Annals of Mathematics B,2015,36(1):105~124 |
| Page view： 1932
Net amount： 1451 |
Authors： |
Song JIANG; Junping YIN; |
Foundation： |
the National Natural Science Foundation of China (Nos. 11101044,
11371065) and the Beijing Center for Mathematics and Information Interdisciplinary Sciences. |
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| Abstract： |
The authors integrate two well-known systems, the R¨ossler and Lorentz systems,
to introduce a new chaotic system, called the Lorentz-R¨ossler system. Then, taking into
account the effect of environmental noise, the authors incorporate white noise in both
R¨ossler 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-R¨ossler 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-R¨ossler system could
be used to design more complex and more secure nonlinear hop-frequence time series. |
Keywords： |
Stochastic differential equations, Rossler-Lorentz systems, Existence,
Pathwise property |
Classification： |
60J65, 34K40 |
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