General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms A model for cell polarisation without mass conservation. 1Nicolas Verschueren * and Alan Champneys † 2 3 Abstract. A system of two Schnakenberg-like reaction-diffusion equations is investigated analytically and nu-4 merically. The system has previously been used as a minimal model for concentrations of GTPases 5 involved in the process of cell polarisation. Source and loss terms are added, breaking the mass 6 conservation, which was shown previously to be responsible for the generation of stable fronts via a 7 so-called wave-pinning mechanism. The extended model gives rise to a unique homogeneous equi-8 librium in the parameter region of interest, which loses stability via a pattern formation, or Turing 9 bifurcation. The bistable character of the reaction terms ensures that this bifurcation is subcrtical 10 for sufficiently small values of the driving parameter multiplying the nonlinear kinetics. This sub-11 criticality leads to the onset of a multitude of localised solutions, through the homoclinic snaking 12 mechanism. As the driving parameter is further decreased, the multitude of solutions transforms 13 into a single pulse through a Belyakov-Devaney transition in which there is the loss of a precursive 14pattern. An asymptotic analysis is used to probe the conservative limit in which the source and 15 loss terms vanish. Matched asymptotic analysis shows that on an infinite domain the pulse solution 16transitions into a pair of fronts, with an additional weak quadratic core and exponential tails. On 17 a finite domain, the core and tails disappear, leading to the mere wave-pinning front and its mirror 18 image.

No abstract

The existence, stability properties, and dynamical evolution of localized spatiotemporal chaos are studied. We provide evidence of spatiotemporal chaotic localized structures in a liquid crystal light valve experiment with optical feedback. The observations are supported by numerical simulations of the Lifshitz model describing the system. This model exhibits coexistence between a uniform state and a spatiotemporal chaotic pattern, which emerge as the necessary ingredients to obtain localized spatiotemporal chaos. In addition, we have derived a simplified model that allows us to unveil the front interaction mechanism at the origin of the localized spatiotemporal chaotic structures.