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Decaying localized structures beyond Turing space in an activator–inhibitor system

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Abstract

We perform numerical simulations beyond Turing space in an activator–inhibitor system involving quadratic and cubic nonlinearities . We show that while all the three fixed points of the system are stable nodes, it exhibits spatially stable patterns as diverse as labyrinths, worms, negatons, and combination of them. The transition among the patterns is found to be dependent on the relative strength (h) of quadratic and cubic couplings. The labyrinths and worms are formed for small values of h while stable negatons are obtained for \(0.0891\le h\le 0.1106\). The negatons start showing decaying behavior for \(h\ge 0.1135\) and, finally they vanish at random positions by emitting remnant solitary waves, yielding a pattern of stable concentric rings. The spatial extension of the concentric rings is found to depend on the initial concentration profile of the decaying negatons. The resulting concentric rings do not decay further due to limitation of numerical precision. We also find that the transient period for each pattern also depends on h.

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Correspondence to Kishore Dutta.

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Talukdar, D., Dutta, K. Decaying localized structures beyond Turing space in an activator–inhibitor system. Eur. Phys. J. Plus 135, 53 (2020). https://doi.org/10.1140/epjp/s13360-019-00063-6

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