https://doi.org/10.1140/epjp/s13360-019-00063-6
Regular Article
Decaying localized structures beyond Turing space in an activator–inhibitor system
Department of Physics, Handique Girls’ College, Guwahati, 781 001, India
* e-mail: kdkishore77@gmail.com
Received:
11
March
2019
Accepted:
21
October
2019
Published online:
13
January
2020
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 
. The negatons start showing decaying behavior for 
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.
© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
