Nonlinear Chaotic Processing Model

TL;DR

This paper presents the nonlinear chaotic processing (NCP) model, a flexible framework for generating complex chaotic maps using basic nonlinear operations, with demonstrated enhanced chaotic properties through various evaluations.

Contribution

The NCP model introduces a novel, extendable framework for creating diverse chaotic maps by combining nonlinear operations, advancing the design of complex chaotic systems.

Findings

Generated chaotic maps exhibit higher Lyapunov exponents

Maps show increased Shannon entropy and correlation dimension

Enhanced initial state sensitivity compared to existing maps

Abstract

Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use existing chaotic maps as seed maps to generate a huge number of new chaotic maps. The proposed NCP model can be easily extended by introducing new nonlinear operations or by arbitrarily combining existing ones. The properties and chaotic behaviors of the NCP model are investigated. To show its effectiveness and usability, as examples, we provide four new chaotic maps generated by the NCP model and evaluate their chaotic performance using Lyapunov exponent, Shannon entropy, correlation dimension and initial state sensitivity. The experimental results show that these chaotic maps have more complex chaotic behaviors than existing ones.