What is a linear harmonic oscillator? And what is a non-linear oscillator?

(N/A) linear harmonic oscillator is a system where the restoring force $F$ acting on a particle is directly proportional to its displacement $x$ from the equilibrium position,expressed as $F = -kx$,where $k$ is a constant.
In a non-linear oscillator,the restoring force is not strictly proportional to the displacement. It may contain higher-order terms of the displacement,such as $x^2, x^3, \dots$,meaning the force is expressed as $F = -kx - ax^2 - bx^3 - \dots$. These systems do not follow simple harmonic motion.