A high-precision numerical method to simulating the fractional-order EI Niño chaotic systems with Riemann–Liouville fractional derivative

Abstract

Chaotic systems arise everywhere in control theory and nonlinear vibration. This paper uses a high-precision numerical approach for capturing chaotic attractors of the fractional EI Ni ño chaotic systems. The numerical results indicate that some of the chaotic attractors of fractional-order systems are topologically equivalent to those discovered in the integer-order systems, and some unusual attractors of fractional EI Ni ño chaotic systems are found by using the present method.

Dynamics and synchronization of a fractional-order hyperchaotic financial system

“…Because the initial conditions have a strong influence on chaotic systems, a slight deviation or disturbance of the initial conditions will have a greater impact on economic development. Therefore, chaotic dynamics models that are compatible with economic principles are still the basis for evaluating and forecasting economic activities [5][6][7][8]. With the improved computational power, the theory of fractional operations has been applied to economics, so the economic system of fractional order has emerged and began to be discussed [9].…”