In a position wave-numbers involving zero and one (together with the most unstable wave-number

)/2 with 2 = 3 . Parameters title= hpu.2013.0021 are 1 = 0.five, two = 0.15, 3 = -0.3, 1 = 1/2, 2 = 1/4, and = -1.45. There's a band of unstable wave-numbers with p (0, computer ), with pc 1.Fig. 19 The emergence of a turbulent phase state in a phase oscillator continuum model. The parameters are these as in Fig. 18 with = 0 for which = 0.63, = 5.16 and = 0.096. The physical domain size is 27 and we've utilised a numerical mesh of 212 points with Matlab ode45 to evolve Eq. (43) with convolutions computed making use of speedy Fourier transforms. As an order parameter describing the system we have chosen | |, where = ( 1 W1 + two W2 ) z + three W3 z7 Heteroclinic AttractorsIn addition to dynamically very simple periodic attractors with varying degrees of clustering, the emergent dynamics of coupled phase oscillator systems for example (32) is often remarkably complicated even in the case of global coupling and similar effects can appear inside a wide array of coupled systems. Inside the case of globally coupled phase oscillators, the dynamical complexity depends only on the phase interaction title= j.toxlet.2015.11.022 function H and the number of oscillators N . Chaotic dynamics [243] can appear in four or more globally coupled phase oscillators for phase interaction functions of adequate complexity. We focus now on attractors that happen to be robust and apparently prevalent in numerous such systems: robust heteroclinic attractors. Within a neuroscience context such attractors have already been investigated under numerous associated names, including slow switching [231, 244?46] exactly where the system evolves towards an attractor that displays slow switching amongst cluster states exactly where theJournal of Mathematical Neuroscience (2016) 6:Web page 61 ofFig. 20 Schematic diagram showing a trajectory x(t) (solid line) approaching element of a robust heteroclinic network in phase space (bold dashed lines). The nodes xi represent equilibria or periodic orbits of saddle type as well as the invariant Ssity of hemodynamic help, as well as the surgical access (Fig. 1) [18. In case] subspaces Pi are forced to exist by model assum.