Cluster synchronization, switching and spatiotemporal coding in a phase oscillator network

Abstract

A network of five globally-coupled identical phase oscillators is considered. Cluster states consisting of two synchronized pairs of oscillators and one singleton are investigated. Forcing the system with non-uniform constant inputs results in regular switches between cluster states. The resultant cyclic sequences of switches (spatiotemporal codes) are studied for different initial conditions and input configurations. Implications on information coding in neural systems are briefly discussed.

Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

“…For a more complex visualization example oscillators in space are coupled (figure 4). A mathematical generator has been applied to generate coupled phase oscillation on data to describe spatial-temporal coding in computational neuroscience (Orosz et al, 2007). As long as the inputs are quantized to the graphs cyclic format, the result of a change to the systems inputs is spatially unpredictable but in general there is a global coherence in terms of the tendency towards an even symmetry in space being retained in the manner of entropic forcing.…”

Computation by Switching in Complex Networks of States

“…If so, which systems are appropriate and how can computations be performed? A broad range of systems exhibit saddle states that are dynamically linked via heteroclinic connections to form complex networks [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. These may be promising candidates for such computations because the dynamics close to heteroclinic networks is intrinsically robust, easily controllable, and provides a large number of state-changing options already for small systems [8,9,12,16].…”

“…A sequence of such connections linking several saddles cyclically is called a heteroclinic cycle. If the dynamical system considered exhibits a certain symmetry, complex heteroclinic networks consisting of interconnected heteroclinic cycles emerge in a robust way.Heteroclinic networks are of high current mathematical interest [1][2][3][4][5]15]. Simultaneously, their specific dynamical features-supporting repetitive switching close to the saddles-pose a promising challenge for the study of information encoding and computation, in particular, in artificial neural systems [6][7][8][9][10][11][12][13][14]16].…”

“…For instance, it becomes more and more clear how information may be encoded by systems with heteroclinic cycles [8,10,11,14,16]. Recent studies even provide insights about how external perturbations may be processed [12,15,16] and hints on how such systems may actually compute using switching among saddles [12]. Nevertheless, it is still far from understood whether and how nonlinear dynamical systems may perform generic computations exploiting their complex networks of states.…”

“…In addition, the signal-induced switching (i) appears as a generic feature of symmetry breaking in systems with heteroclinic connections, (ii) yields intrinsic self-corrections due to cyclic repetitions, and (iii) is robust to distractions and simultaneously sensitive to distinct external signals. Given these features, this computational paradigm provides a natural and flexible approach for performing logic operations in a variety of systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”