Theoretical study of chaotic jumping of liquid crystal elastomer ball under periodic illumination

Chaotic systems exhibit distinctive characteristics, including sensitivity to initial conditions and ergodicity within the domain of attraction. These features offer significant potential for applications in biomimetic machinery, medical instruments, and other domains. This paper focuses on exploring and analyzing a distinct class of a chaotic jumping systems composed of a liquid crystal elastomer (LCE) ball and an elastic substrate. By periodic illumination, the light-responsive LCE ball can be converted from a stationary state to a motion state. The coupled motion process of contact-expansion and jump of the LCE ball under periodic illumination is described, and the mechanism of the contact-expansion work compensating for the damping dissipation of the system and maintaining the sustained motion of the LCE ball is revealed. The numerical results show that the jumping behavior of the LCE ball is affected by system parameters, such as period and intensity of illumination, gravitational acceleration, elastic modulus, contraction coefficient and damping coefficient. The bifurcation diagram illustrates that by manipulating the system parameters, the LCE ball can transition between periodic motion and chaotic motion. The present research results can deepen the understanding of active materials based on the dynamics of chaotic systems, and provide guidance for the research on chaotic encryption communication, chaotic self-cleaning, chaotic agitation and so on.