# Chaos suppression in fractional order systems using state-dependent noise

## TL;DR

This paper explores how state-dependent noise affects bifurcation in fractional order chaotic systems, revealing that such noise can inhibit bifurcation processes and impact system stability and reliability.

## Contribution

It provides the first investigation into the influence of state-dependent noise on bifurcation in fractional order chaotic systems, supported by circuit implementation and numerical analysis.

## Key findings

- State-dependent noise inhibits period doubling bifurcations.
- Results impact control, communication, and power system reliability.
- Numerical simulations confirm the noise's stabilizing effect.

## Abstract

Noise play a creative role in the evolution of periodic and complex systems which are essential for continuous performance of the system. The interaction of noise generated within one component of a chaotic system with other component in a linear or nonlinear interaction is crucial for system performance and stability. These types of noise are inherent, natural and insidious. This study investigates the effect of state-dependent noise on the bifurcation of two chaotic systems. Circuit realization of the systems were implemented. Numerical simulations were carried out to investigate the influence of state dependent noise on the bifurcation structure of the Chen and Arneodo-Coullet fractional order chaotic systems. Results obtained showed that state dependent noise inhibit the period doubling cascade bifurcation structure of the two systems. These results poses serious challenges to system reliability of chaotic systems in control design, secure communication and power systems.