Achilles' heel of a traveling pulse subject to a local external stimulus

Abstract

The response of a traveling pulse to a local external stimulus is considered numerically for a modified three-component Oregonator, which is a model system for the photosensitive Belousov-Zhabotinsky (BZ) reaction. The traveling pulse is traced and constantly stimulated, with the distance between the pulse and the stimulus being kept constant. We are interested in the minimal strength of the spatially localized stimulus in order to eliminate the pulse. The use of a stimulus of small width allows us to detect the point in the pulse most sensitive to the external stimulus, referred to as the "Achilles' heel" of the traveling pulse, at which minimal strength of stimulus causes a collapse of the pulse. Our findings are demonstrated experimentally as well with the photosensitive BZ reaction.

Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators

“…We use the typical parameter set for the limit cycle oscillation: ε = 0.1, δ = 0.001, f = 1.0, and q = 0.01. The diffusion coefficients for u, v, w are assumed to be the same positive constant D. We describe the light feedback effect by adding sφ to the equation for v, where φ is the average concentration of w 1 and w 2 and s is a positive constant corresponding to the feedback strength [3,4,8]. We consider s and D as bifurcation parameters.…”

“…In fact, Mihaliuk et al reported that they localized the traveling wave and controlled its movements [5][6][7]. Nishi et al reported that they eliminated the propagation wave [8]. In the above reports, they introduced theoretical studies using the Oregonator model.…”

Originating Point of Traveling Waves on a Spherical Field Dependent on the Nature of Substrate Surface

“…Wave propagation has been investigated to understand the nature of excitation or oscillation and the intrinsic mechanism of signal transduction in biological systems, such as Ca 2+ waves and nerve impulses. The Belousov–Zhabotinsky (BZ) reaction has been employed as a representative chemical oscillatory system. − Several types of experimental systems for the BZ reaction have been developed to clarify nonlinear phenomena, and various types of spatiotemporal patterns are well controlled by external stimuli such as light irradiation − and electric fields. − …”

Switching between Two Oscillatory States Depending on the Electrical Potential

“…Under nonequilibrium conditions, reaction–diffusion systems can show a wealth of oscillatory phenomena and spatiotemporal patterns such as circadian rhythms and animal coat patterns. − In this context, the Belousov–Zhabotinsky (BZ) reaction, , which self-organizes spatiotemporal patterns based on an autocatalytic reaction, is a frequently studied experimental system and continues to offer valuable insights into the basic mechanisms of rhythmic phenomena and pattern formation in living systems. Much of this progress involved the application of external perturbation, such as light irradiation − and electric fields, − which provided deeper insights into the mechanisms of dissipative pattern formation and also suggested effective control procedure for their spatiotemporal dynamics. For example, S̆evčíková et al reported that the speed, directions, and behavior, such as splitting, of propagating chemical waves can be controlled by the application of electric field. − …”