Theoretical study and circuit implementation of three chain-coupled self-driven Duffing oscillators

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Complex Systems

Background:

• Coupled oscillators exhibit complex behaviors.
• Duffing oscillators are a fundamental model in nonlinear dynamics.
• Understanding transitions to chaos is crucial for many scientific fields.

Purpose of the Study:

• To investigate the dynamics of three chain-coupled self-driven Duffing oscillators.
• To analyze the emergence of oscillations and multi-spiral chaos.
• To explore bifurcations and chaotic attractors in this novel system.

Main Methods:

• Computer integration of state equations.
• Analysis using Lyapunov exponent plots, bifurcation diagrams, basins of attraction, and phase portraits.
• Electronic circuit implementation and simulation using Orcad-PSpice.
• Microcontroller-based hardware realization.

Main Results:

• Identified eight equilibrium points exhibiting multiple Hopf bifurcations.
• Observed coexistence of eight bifurcation branches.
• Discovered a multitude of coexisting oscillation types.
• Characterized a six-spiral chaotic attractor.

Conclusions:

• The novel system of three chain-coupled Duffing oscillators displays rich nonlinear dynamics.
• The theoretical findings are validated through circuit simulations and hardware realization.
• The study demonstrates the practical feasibility of complex coupled oscillator systems.