An interval chaos insight to iterative decomposition method for Rossler differential equation by considering stable uncertain coefficients

Generally, in most applications of engineering, the parameters of the mathematical models are considered deterministic. Although, in practice, there are always some uncertainties in the model parameters; these uncertainties may be made wrong representation of the mathematical model of the system. These uncertainties can be generated from different reasons like measurement error, inhomogeneity of the process, chaotic behavior of systems, etc. This problem leads researchers to study these uncertainties and propose solutions for this problem. The iterative analysis is a method that can be utilized to solve these kinds of problems. In this paper, a new combined method based on interval chaotic and iterative decomposition method is proposed. The validation of the proposed method is performed on a chaotic Rossler system in stable Intervals. The simulation results are applied on ۲ practical case studies and the results are compared with the interval Chebyshev method and RungeKutta method of order four (RK۴) method. The final results showed that the proposed method has a good performance in finding the confidence interval for the Rossler models with interval uncertainties; the results also showed that the proposed method can handle the wrapping effect in a better manner to sharpen the range of non-monotonic interval.

Keywords:

Chaos theory , Chaotic systems , Interval decomposition method , Rossler differential equations