Stability of Fixed Points and Chaos in Fractional Systems

Abstract

In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0<\alpha <2$. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

24 pages 3 figures. arXiv admin note: substantial text overlap with arXiv:1709.00093

References in corpus (3)

• Discrete-Time Fractional Variational Problems
• Fractional $h$-difference equations arising from the calculus of variations
• Long and Short Memory in Economics: Fractional-Order Difference and Differentiation

Cited by in corpus (6)

• General Fractional Dynamics
• Fractional order logistic map; Numerical approach
• Asymptotic cycles in fractional maps of arbitrary positive orders
• Asymptotic cycles in fractional generalizations of multidimensional maps
• Evolution of Systems with Power-Law Memory: Do We Have to Die?
• Stability analysis of fixed point of fractional-order coupled map lattices