Multi-composition-exponential-modulo chaotification model.

Area of Science:

• Dynamical Systems and Chaos Theory
• Computational Mathematics
• Cryptography

Background:

• Chaotification techniques are crucial for generating complex dynamical systems.
• Exponential functions offer flexibility in designing novel chaotic maps.
• Understanding fixed points and Lyapunov exponents is key to characterizing chaotic behavior.

Purpose of the Study:

• To introduce a new chaotification technique based on the composition of exponential functions.
• To explore the design freedom offered by this technique for creating diverse chaotic map families.
• To investigate the analytical and numerical properties of the designed maps and their potential applications.

Main Methods:

• Composition of exponential functions with offset boosting and a seed function in the exponent.
• Analytical derivation of Lyapunov exponent expressions and fixed point analysis.
• Numerical simulations including cobweb, fixed point, bifurcation, and Lyapunov exponent diagrams.

Main Results:

• Three distinct chaotic map examples were designed from the general family.
• Observed behaviors include the absence of fixed points, leading to hidden attractors.
• Demonstrated robust chaos and successful application in pseudorandom bit generation.

Conclusions:

• The proposed chaotification technique provides significant design freedom.
• The designed maps exhibit interesting dynamical properties, including hidden attractors and robust chaos.
• This family of maps shows considerable promise for applications in pseudorandom number generation and further research.