Browsing by Author "Ashwin, Peter"
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The 1 : √2 mode interaction and heteroclinic networks in Boussinesq convection
Podvigina, Olga; Ashwin, Peter (Elsevier, 2007)Methods of equivariant bifurcation theory are applied to Boussinesq convection in a plane layer with stressfree horizontal boundaries and an imposed square lattice periodicity in the horizontal directions. We consider ... 
Acceleration of onedimensional mixing by discontinuous mappings
Ashwin, Peter; Nicol, Matthew; Kirkby, Norman (Elsevier, 2002)The paper considers a simple class of models for mixing of a passive tracer into a bulk material that is essentially one dimensional. We examine the relative rates of mixing due to diffusion, stretch and fold operations ... 
Anisotropic properties of riddled basins
Ashwin, Peter; Breakspear, Michael (Elsevier, 2001)We consider some general properties of chaotic attractors with riddled basins of attraction (basins with positive measure but open dense complements) in dynamical systems with symmetries. We investigate how a basin of ... 
Attractors of a randomly forced electronic oscillator
Ashwin, Peter (Elsevier, 1999)This paper examines an electronic oscillator forced by a pseudorandom noise signal. We give evidence of the existence of one or more random attractors for the system depending on noise amplitude and system parameters. ... 
Bidirectional transport and pulsing states in a multilane ASEP model
Lin, Congping; Steinberg, Gero; Ashwin, Peter (IOP Publishing, 2011)In this paper, we introduce an ASEPlike transport model for bidirectional motion of particles on a multilane lattice. The model is motivated by {\em in vivo} experiments on organelle motility along a microtubule (MT), ... 
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri (Elsevier, 2008)We study the bifurcation and dynamical behaviour of the system of N globally coupled identical phase oscillators introduced by Hansel, Mato and Meunier, in the cases N=3 and N=4. This model has been found to exhibit robust ... 
Blowout bifurcation in a system of coupled chaotic lasers
Ashwin, Peter; Terry, John R.; Thornburg, K. Scott; Roy, Rajarshi (American Physical Society, 1998)We show that loss of synchronization of two identical coupled chaotic class B lasers can occur via a blowout bifurcation. This occurs when a transverse Lyapunov exponent governing the stability of a synchronized subspace ... 
Chaos in symmetric phase oscillator networks
Bick, Christian; Timme, Marc; Paulikat, Danilo; Rathlev, Dirk; Ashwin, Peter (American Physical Society, 2011)Phasecoupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic ... 
Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators
Bick, Christian; Ashwin, Peter (arXiv.org, 20150929)Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recentlyintroduced ... 
Chimera states in networks of phase oscillators: the case of two small populations
Panaggio, Mark J.; Abrams, Daniel M.; Ashwin, Peter; Laing, Carlo R. (Arxiv.org, 20150812)Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators ... 
Classification of robust heteroclinic cycles for vector fields in R3 with symmetry
Hawker, David; Ashwin, Peter (Institute of Physics, 2005)We consider a classification of robust heteroclinic cycles in the positive octant of R3 under the action of the symmetry group (Z2)3. We introduce a coding system to represent different classes up to a topological equivalence, ... 
Cone exchange transformations and boundedness of orbits
Ashwin, Peter; Goetz, Arek (Cambridge University Press, 2010)We introduce a class of twodimensional piecewise isometries on the plane that we refer to as cone exchange transformations (CETs). These are generalizations of interval exchange transformations (IETs) to 2D unbounded ... 
Convergence to local random attractors
Ashwin, Peter; Ochs, Gunter (Taylor & Francis, 2003)Random attractors allow one to classify qualitative and quantitative aspects of the longtime behaviour of stochastically forced systems viewed as random dynamical systems (RDS) in an analogous way to attractors for ... 
Criteria for robustness of heteroclinic cycles in neural microcircuits.
Ashwin, Peter; Karabacak, Ozkan; Nowotny, Thomas (BioMed Central / SpringerOpen, 2011)We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in LotkaVolterratype ... 
Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection
Ashwin, Peter; Rucklidge, Alastair M. (Elsevier, 1998)We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant ... 
Cycling chaotic attractors in two models for dynamics with invariant subspaces
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (American Institute of Physics, 2004)Nonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddletype invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors ... 
Decelerating defects and nonergodic critical behaviour in a unidirectionally coupled map lattice
Ashwin, Peter; Sturman, Rob (Elsevier, 2003)We examine a coupled map lattice (CML) consisting of an infinite chain of logistic maps coupled in one direction by inhibitory coupling. We find that for sufficiently strong coupling strength there are dynamical states ... 
Designing heteroclinic and excitable networks in phase space using two populations of coupled cells
Ashwin, Peter; Postlethwaite, Claire (Springer Verlag, 20150610)We give a method for realizing an arbitrary directed graph (with no onecycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is ... 
Designing the dynamics of globally coupled oscillators
Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter (Oxford University Press, 2009)A method for designing cluster states with prescribed stability is presented for coupled phase oscillator systems with alltoall coupling. We determine criteria for the coupling function that ensure the existence and ... 
Discrete computation using a perturbed heteroclinic network
Ashwin, Peter; Borresen, Jon (Elsevier, 2005)Transient synchronization into clusters appears in many biological and physical systems and seems to be important for computation within neural systems. In this paper we show how one can robustly and effectively perform ...