Spikes and localised patterns for a novel Schnakenberg model in the semi-strong interaction regime

التفاصيل البيبلوغرافية
العنوان: Spikes and localised patterns for a novel Schnakenberg model in the semi-strong interaction regime
المؤلفون: Theodore Kolokolnikov, Fahad Al Saadi, Chunyi Gai, Alan R Champneys
المصدر: University of Bristol-PURE
مصطلحات موضوعية: Physics, Chemical physics, Applied Mathematics, 0103 physical sciences, Strong interaction, 010306 general physics, 01 natural sciences, 010305 fluids & plasmas
الوصف: An analysis is undertaken of the formation and stability of localised patterns in a 1D Schanckenberg model, with source terms in both the activator and inhibitor fields. The aim is to illustrate the connection between semi-strong asymptotic analysis and the theory of localised pattern formation within a pinning region created by a subcritical Turing bifurcation. A two-parameter bifurcation diagram of homogeneous, periodic and localised patterns is obtained numerically. A natural asymptotic scaling for semi-strong interaction theory is found where an activator source term \[a = O(\varepsilon )\] and the inhibitor source \[b = O({\varepsilon ^2})\], with ε2 being the diffusion ratio. The theory predicts a fold of spike solutions leading to onset of localised patterns upon increase of b from zero. Non-local eigenvalue arguments show that both branches emanating from the fold are unstable, with the higher intensity branch becoming stable through a Hopf bifurcation as b increases beyond the \[O(\varepsilon )\] regime. All analytical results are found to agree with numerics. In particular, the asymptotic expression for the fold is found to be accurate beyond its region of validity, and its extension into the pinning region is found to form the low b boundary of the so-called homoclinic snaking region. Further numerical results point to both sub and supercritical Hopf bifurcation and novel spikeinsertion dynamics.
تدمد: 0956-7925
URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eef74d20cbb962cac445660f15072f42
https://research-information.bris.ac.uk/en/publications/f832837c-10eb-4bd8-8cb5-147866c31c0e
Rights: CLOSED
رقم الانضمام: edsair.doi.dedup.....eef74d20cbb962cac445660f15072f42
قاعدة البيانات: OpenAIRE