Investigating the nonlinear dynamics of photosensitive Belousov–Zhabotinsky gels via bifurcation analyses

Controlling the dynamics of active stimuli-responsive smart materials is essential to replicate the biomimetic functionalities at different length scales for a variety of biological systems-based applications. Photosensitive Belousov–Zhabotinsky (BZ) gels, powered by a nonlinear chemical oscillator, called a BZ reaction are one of the stimuli-responsive smart materials in demand due to their ability to continuously transduce chemical oscillations into mechanical deformations. The chemical oscillations in a BZ reaction and subsequent mechanical oscillations in photosensitive BZ gels occur due to the redox cycle of photosensitive ruthenium complex-based catalysts. In this work, our objective is to identify how the behavior of photosensitive BZ gels can be tuned and used for biomimetic applications by investigating its dynamical characteristics using bifurcation analyses. Specifically, we use the normal form approach and perform linear and nonlinear stability analyses to identify high-order bifurcations by computing higher-order Lyapunov and frequency coefficients. We revealed the existence of domains that encompass coexisting stable and unstable limit cycles (LCs), which merge to form a semi-stable LC at the limit point of cycle (LPC). Their existence shows how a slight variation in the BZ gel recipe can significantly alter its dynamics. Subsequently, we quantify the amplitude and frequency of oscillations in different domains under the effect of variation of BZ reaction formulations. We believe that the outcomes of our work serve as an efficient template for the design and control of BZ gel-based applications. The usage of a normal form and a systematic representation of nonlinear dynamics allow our framework to be extended for other nonlinear dynamical systems.