Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback

Abstract

We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov-Zhabotinsky (BZ) reaction. GNF is established by homogeneous illumination of the 1D array with the light intensity proportional to the number of BZ droplets in the oxidized state with the coefficient of proportionality ge. MDs are immersed in the continuous oil phase and diffusively coupled with the neighboring droplets via inhibitor Br2 which is soluble in the oil phase. At chosen concentrations of the BZ reactants, illumination suppresses the BZ oscillators. Without GNF, or at a very small ge < 0.29, local inhibitory coupling leads to out-of-phase oscillations of the neighboring BZ droplets with an almost constant phase shift Δφ between them, which makes a space-time plot of the BZ MDs look like a staircase. At 0.3 < ge < 0.6, regular oscillatory clusters consisting of distant BZ MDs (mostly 5-6 phase clusters) emerge. At 0.6 ≤ ge ≤ 1.0, chaotic clusters are observed. At 1.2 < ge < 1.8, regular (mostly 3-4-phase) clusters emerge again. At 1.8 < ge < (3-4), complex clusters with different (but multiple) periods of oscillation are observed. At the same time, some droplets stop oscillating. At large enough ge (>4), in the region of two-phase clusters (with several suppressed BZ MDs), final patterns seem to resemble the initial patterns. Intensive computer simulations with the ordinary differential equations support experimental results.

A memristive non-smooth dynamical system with coexistence of bimodule periodic oscillation

“…In recent years, scholars have carried out in-depth research on bursting oscillations of various dynamical systems by the fast-slow analysis method, and have achieved a series of results. For example, Bao et al [13] revealed chaotic bursting oscillations and the generation mechanism of the two fast and one slow Morris-Lecar neuron model, and verified the correctness of the theoretical analysis from the hardware circuit; Proskurkin et al [14] studied the bursting oscillation phenomenon in chemical reaction systems; Han et al [15] studied the bursting behavior of the parameter-excited Lorenz system and reported the chaotic bursting phenomenon caused by the bifurcation delay and chaotic crisis; Ma et al [16] revealed the complex bursting structure induced by delayed pitchfork bifurcation in the periodically excited Jerk circuit; Han et al [17] revealed two novel bursting oscillation patterns induced by turnover-pitchfork-hysteresis and compoundpitchfork by introducing multi-frequency parameter excitation in the Duffing oscillator; Wei et al [18] studied the bursting dynamics behavior of mechanical systems under the combination of parametric excitation and external excitation, and revealed the complex cascaded bursting pattern caused by Hopf bifurcation and homoclinic bifurcation. On the other hand, bursting oscillations and their formation mechanism in non-smooth systems based on fast-slow analysis methods have also received extensive attention.…”

Fabrication of New Belousov–Zhabotinsky Micro-Oscillators on the Basis of Silica Gel Beads

“…Our setup is similar to that used previously − and is exhibited in Figure . A Petri dish with the BZ beads (in the BZ solution or in the oil phase) is illuminated from below with an light-emitting diode (LED) light source through an interference filter (Edmund Optics, λ = 450 nm).…”

Impact of PDMS-Based Microfluidics on Belousov–Zhabotinsky Chemical Oscillators

“…Compartmentalization of the oscillatory Belousov–Zhabotinsky (BZ) chemical reaction as aqueous drops in a continuous oil phase serves as a means to create networks in which either inhibitory or excitatory BZ species permeate from one BZ compartment to another. − In an alternative approach, we demonstrated the engineering of reaction–diffusion networks employing the BZ reaction that were capable of producing a wide variety of spatiotemporal patterns, including that of central pattern generators found in living organisms. To build these networks, we employed methods from soft lithography to fabricate diffusively coupled networks using the elastomer polydimethylsiloxane (PDMS). , This method offers numerous advantages over the use of drops to create networks, and we demonstrated control of (i) the topology of the network, the (ii) boundary and (iii) initial conditions, (iv) the volume of each reactor, (v) the coupling strength, and (vi) whether the coupling was of an inhibitory or excitatory nature .…”