A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

Area of Science:

• Nonlinear Dynamics
• Circuit Theory
• Chaos Theory

Background:

• Existing 5-D systems (e.g., Sprott B, Lorentz) offer complex dynamics but can be intricate.
• The development of simpler systems is crucial for understanding and applying chaotic phenomena.

Purpose of the Study:

• To propose a novel, simplified 5-D autonomous hyperjerk circuit.
• To investigate the complex dynamical behaviors, including chaos and multistability, of this new system.

Main Methods:

• Design of a 5-D hyperjerk circuit utilizing a hyperbolic sine function and two diodes.
• Bifurcation analysis to explore the system's dynamics.
• Phase space analysis to identify coexisting attractors.
• Pspice circuit simulations for validation.

Main Results:

• The proposed system is the simplest 5-D system with complex dynamics reported to date.
• The system exhibits a single equilibrium point and can display periodic and chaotic behaviors.
• Multistability is observed, with up to seven coexisting attractors dependent on initial conditions.

Conclusions:

• The novel 5-D hyperjerk circuit offers a simplified platform for studying complex nonlinear dynamics.
• The discovered rich dynamics, particularly multistability, present new avenues for research in chaotic systems.
• Circuit simulations confirm the theoretical findings, validating the system's behavior.