THEORETICAL AND NUMERICAL INVESTIGATION OF COMPLEXITIES IN FRACTIONAL-ORDER CHAOTIC SYSTEM HAVING TORUS ATTRACTORS
Changjin Xu, Mati ur Rahman, Bibi Fatima, Yeliz Karaca
Abstract
This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated covering existence uniqueness, attractor projection, time series analysis and sensitivity towards initial values. 4-torus attractor coexistence is observed with different fractional orders. The numerical scheme is used to approximate the system numerically which is based on the Newton polynomials. The numerical illustrations of the system demonstrate that moving from higher fractional-order to lower fractional-order affects the dynamics of the system significantly, which in turn has a shrinking impact on the geometry of the oscillatory range. The emergence of new oscillations can also be observed at lower fractional orders, revealing that the system oscillates rapidly with lower amplitudes as compared to those having higher fractional orders.