The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy

Abstract

The dynamics of the Caputo-fractional variable-order difference form of the Tinkerbell map are studied. The phase portraits, bifurcation, and largest Lyapunov exponent (LLE) were employed to demonstrate the presence of chaos over a different fractional variable-order and establish the nature of the dynamics. In addition, the 0–1 test tool was used to detect chaos. Finally, the numerical results were confirmed using the approximate entropy.

Keywords

• fractional variable-order
• Tinkerbell map
• chaos
• bifurcation
• Lyapunov exponents
• 0–1 test