Random symmetry breaking and freezing in chaotic networks

Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a nonchaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the sign amplitude of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneous with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the size of the network. Results are exemplified by a network of modified Duffing oscillators with infinite range pseudoinverse delayed interactions.