Stabelity analysis to predict dynamic bhevior of self-oscillating polymer gels

Abstract

Self-oscillating polymer gels find their applications in smart materials that can autonomously produce mechanical deformation without the aid of external stimuli. These polymer gels are intrinsically driven by chemical oscillatory BZ (Belousov Zhabotinsky) reaction and thus are able to transducer chemical energy into mechanical work. The BZ reaction is photosensitive, and therefore light provides a stimulus for controlling the dynamic behavior of BZ gels. It has been established that light has an inhibitory effect on the mechanical oscillations of BZ gels. The switching from stable, non-oscillatory state to oscillatory state can be mathematically explained by the occurrence of a Hopf Bifurcation. Using linear stability and normal form analysis, we predict the conditions at which the gel switches from non-oscillatory to oscillatory state. We also characterize the nature of Hopf Bifurcation and identify other bifurcations which govern the dynamic behavior ofBZ gels. The switching of behavior from one nature of Hopf ifurcation to another or in other words, the stability of the periodic orbits has been established quantitatively by means of Lyapunov exponents. For this, first and second Lyapunov exponents have been derived. The presented approach not only allows us to understand non-linear dynamical systems but also enables us to predict their behavior. Our findings can thus be used to design new synthetic materials with tailor made properties.