Design of Initial Value Control for Modified Lorenz‐Stenflo System

Abstract

For the sake of complexity, unpredictability, and exceeding sensitivity to initial conditions in the chaotic systems, there were many studies for information encryption of chaotic systems in recent years. Enhancing the security in information encryption of chaotic systems, an initial value control circuit for chaotic systems is proposed in this paper. By way of changing the initial value, we can change the behavior of chaotic systems and also change the key of information encryption. An analog circuit is implemented to verify the initial value control circuit design.

Machine Learning in Chaos-Based Encryption: Theory, Implementations, and Applications

“…This modified system successfully captures the essential behavior of the Lorenz attractor, including the generation of the butterfly effect, as well as modified and unsymmetrical Lorenz systems. Additionally, researchers have proposed various other variations of the Lorenz system, such as the fourdimensional Lorenz-Stenflo system [27], [28] with four parameters, aimed at improving stability and unpredictability. Table 1 summarizes continuous-time chaos approaches with the equations that can produce continuous chaos, along with their implementation based on scroll type and function.…”

“…x ′ = σ(y − x) Modified Lorenz [24], [25], [26] y ′ = K(β − z) + m Double Scroll Operational Transconductance Amplifier z ′ = (|x| − ρz) x ′ = σ(y − x) + λω Lorenz Stenflo [27], [28] y ′ = (β − z)x − θy) Multi Scroll Operational Transconductance Amplifier, Product z ′ = xy − ϵz ω ′ = −x − ρω *: λ σ, β, ϵ, θ and ρ are parameters whose choice of value results in a chaotic system. K is a bipolar switching constant which is 1 for x ≥ 0 and -1 for x < 0 due to their use of linear segments with abrupt transitions, thereby yielding complex behavior contingent upon their specific piecewise-linear structure.…”