Chaotic Attractors in Quadratic Discrete Tinkerbell System With Non-Commensurate Fractional Variable-Orders: Complexity, Chaos and Entropy*

This manuscript analyzes the dynamical properties of the incommensurate variable fractional discrete Tinkerbell system. Through time evolution of the states, phase portraits, lyapunov exponents and bifurcation diagrams, it is indicated that the two dimensional incommensurate fractional variable-order Tinkerbell map with discrete time exhibits chaotic and periodic behaviour. The approximation entropy is also used to estimate the complexity of the incommensurate variable fractional-order Tinkerbell system with discrete time. Finally, the 0-1 test plots of the presented discrete Tinkerbell map with incommensurate variable fractional-order validate the findings from the largest lyapunov exponents, bifurcation diagrams and approximate entropy. Numerical results are provided out to simulate the effectiveness of the approach described herein.