NUMERICAL SIMULATION OF THE FRACTIONAL-ORDER RÖSSLER CHAOTIC SYSTEMS WITH GRÜNWALD–LETNIKOV FRACTIONAL DERIVATIVE

Abstract

In recent years, scholars have studied the chaotic behavior in the fractional dynamic systems and found that the fractional dynamic systems have unique properties that the integer dynamic systems do not have. Therefore, the numerical simulation of fractional chaotic systems is very important. This paper introduces a high-precision numerical method for the fractional-order Rössler chaotic systems. Complex dynamic behavior of the fractional-order Rössler chaotic systems is shown by using the present method. We observe some novel dynamic behaviors in numerical simulation which are unlike any that have been previously found in numerical experiments or theoretical studies. The simulation results of numerical experiments demonstrate the effectiveness of the present method.