# A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

## TL;DR

This paper introduces a new fractional-order chaotic system that exhibits both self-excited and hidden attractors, with complex dynamics and potential applications in random number generation.

## Contribution

The novelty lies in the system's ability to generate multiple families of attractors, including a 'hurricane'-shaped hidden attractor and multistability, using a single parameter.

## Key findings

- The system can produce self-excited and hidden attractors, including coexisting hidden attractors.
- A no-equilibrium system with a 'hurricane'-like hidden attractor is observed for specific parameter values.
- A pseudo-random number generator is designed based on the hidden chaotic dynamics.

## Abstract

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a ‘hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.