An Approach for the Generation of an Nth-Order Chaotic System with Hyperbolic Sine

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Electrical Engineering

Background:

• Chaotic systems exhibiting hyperbolic sine nonlinearity are a recent focus in research.
• Existing methods for generating such systems may lack simplicity in implementation.
• There is a need for straightforward methods to construct chaotic systems with specific nonlinearities.

Purpose of the Study:

• To introduce a novel approach for generating simple chaotic systems with hyperbolic sine nonlinearity.
• To demonstrate the construction of nth-order chaotic systems using ordinary differential equations (ODEs).
• To present a physically simple electrical circuit implementation for these chaotic systems.

Main Methods:

• Utilizing nth-order ordinary differential equations (ODEs) to define the chaotic systems.
• Employing two back-to-back diodes to model hyperbolic sine nonlinearity, avoiding complex circuits.
• Verifying the proposed method with fourth-order, fifth-order, and tenth-order chaotic system examples.

Main Results:

• A new, systematic approach for constructing chaotic systems with hyperbolic sine nonlinearity was successfully developed.
• The proposed method allows for the generation of chaotic systems of any desired order.
• Demonstrated that simple electrical circuits using two diodes can effectively realize these chaotic systems.

Conclusions:

• The presented method offers a straightforward way to generate simple chaotic systems with hyperbolic sine nonlinearity.
• The use of back-to-back diodes provides a physically simple and cost-effective circuit implementation.
• These systems achieve a balance between analytical complexity and physical simplicity, making them suitable for research and application.