We analyze two classes of Kuramoto models on spheres that have been introduced in previous studies. Our analysis is restricted to ensembles identical oscillators with the global coupling. In such a setup, an additional assumption initial distribution uniform sphere, one can derive equations for order parameters closed form. The rate synchronization real model depends dimension sphere. Specifica...

The heart rate of crustaceans changes with variations in ambient temperature within the normal environmental range (Maynard, 1960). The temperature coefficient (Q10) of the heart rate of crabs over the range 4­19 °C is about 2 (Florey and Kriebel, 1974). There are few studies of the heart response to a rapid change in temperature, although aquatic crustaceans often meet with warm or col...

We consider a Filippov system formed from N coupled phase oscillators similar to the Kuramoto model but using a periodic sawtooth in place of the sine wave. A Hebbian rule based interaction provides for a phase oscillator associative memory network where the memorized patterns are stored as phase-locked limit-cycle attractors. AMS (MOS) Subject Classification. 37N25.

Spatiotemporally chaotic dynamics of a Kuramoto–Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as an accurate guide to the highdimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics. PACS nu...

In this paper we summarize recent advances in the controlled alteration of synchronization in networks of interconnected Kuramoto oscillators. Motivated by neuroscience applications, and in particular by the deep brain stimulation treatment for Parkinson’s disease, we show that a scalar signal, proportional to the mean behaviour of the oscillators population, may either desynchronize or inhibit...