Controlling the transition between the Turing and antispiral patterns by using time-delayed-feedback

TL;DR

This paper investigates how time-delayed feedback can be used to control and induce transitions between Turing and antispiral patterns in a FitzHugh-Nagumo model, revealing the role of delay in pattern formation.

Contribution

It introduces a novel control method using time delay to manipulate pattern transitions between Turing and antispiral structures in reaction-diffusion systems.

Findings

Time delay can induce transitions between Turing and antispiral patterns.

Different feedback parameters lead to various pattern formations.

The dual-mode antispiral results from competition between Turing and Hopf instabilities.

Abstract

The controllable transition between the Turing and antispiral patterns is studied by using time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as perturbation and analyze the effect of the time delay on the Turing and Hopf instabilities near the Turing-Hopf codimension-two phase space. Numerical simulations show the transition between the Turing patterns (hexagon, stripe, and honeycomb), the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.