Some stochastic chaotic attractors with global derivative and stochastic fractal mapping: Existence, uniqueness and applications

Abstract

One of the great ability of humans is to use mathematical formulas to replicate what they see in their daily activities, they start with simple models, when these models are unable to achieve their goals and they modify or replace them with more complex mathematical formulas. Chaos has been modelled using classical differential operators, classical with fractional orders. On the other hand, many mathematical mapping have been used to simulate some fractals behaviours. In this paper, in order to capture more fractal and chaos behaviours, we introduce the notion of chaos stochastic models and fractal stochastic mapping. We additionally present the conditions of existence and uniqueness of chaos‐stochastic models. Some numerical simulations are presented to help see the effect of stochastic functions.