The Duffing oscillator is a mathematical model that describes a nonlinear second-order differential equation representing a damped-driven harmonic oscillator. It exhibits complex behavior, including periodic and chaotic motion, making it a fundamental example in nonlinear dynamics and chaos theory. In the Duffing oscillator equation, the system includes terms representing linear and cubic restoring forces, damping, and an external driving force. This model accounts for a spring’s nonlinear stiffness, unlike a simple harmonic oscillator with linear restoring force. The behavior of the Duffing oscillator can include a wide range of phenomena, from simple periodic motion to more complex behaviors such as bifurcations, chaotic attractors, and chaotic behavior arising from nonlinearity.