Clusters in an assembly of globally coupled bistable oscillators

Abstract

We study the dynamics of an assembly of globally coupled bistable elements. We show that bistability of elements results in some new features of clustering in the assembly when there is global coupling. We provide conditions for the existence of stable amplitude-phase clusters and splay-phase states.PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems

Double-well chimeras in 2D lattice of chaotic bistable elements

“…Interaction of nonlinear elements constituting complex systems results in a great variety of dynamical regimes and spatial structures. These questions are covered in monographs [1,2,3,4,5,6,9,10,7,8] and in many articles (for example, [11,12,13,14,15,16,17,18,19,20,21,22]). In these and other works it is shown that one of the main features of nonlinear networks and spatiallyorganized active systems is the formation of patterns, such as synchronization clusters, spatial intermittency, steady state patterns, spatial chaos, various types of regular and chaotic wave processes, for example, spiral waves.…”

Cloning of Chimera States in a Large Short-term Coupled Multiplex Network of Relaxation Oscillators

“…Let O sn (u 1 = u 0 1 , u 2 = u 0 2 ) ∈ S ∆ 8 be one of such exit points (see Figure 5B). Since the fast and slow trajectories of system (4) are glued together on S ∆ 8 , the point O sn is also the equilibrium state of the fast system (5). From this condition we find…”

“…Study of the formation of chimera states, i.e., peculiar types of hybrid states consisting of oscillators with coherent and incoherent behavior is one of the hot problems of the modern non-linear dynamics. To date, the chimera states have been discovered not only in a variety of theoretical papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], but also in experimental systems of various natures, for example, mechanical [19][20][21][22], optical [23,24], chemical [25][26][27][28][29], and radiotechnical ones [30][31][32][33]. Similar states have also been registered in the neural activity of animal brain networks [34,35].…”

“…Any its element, S ∆ j , defines a curve, where the fast and slow trajectories are stitched. According to GPST, each equilibrium state of fast subsystem (5) [and so (7)] in the phase space R 4 of system (4) corresponds to a submanifold, whose stability with respect to the trajectories of the fast subsystem coincides with the stability of the corresponding equilibrium state. Since the coordinates of the equilibrium states of system (5) depend on two parameters v 0 1 and v 0 2 , any such equilibrium state corresponds to a two-dimensional submanifold in the phase space of (4).…”

Phase Resetting, Clusters, and Waves in a Lattice of Coupled Oscillatory Units

“…Lattice systems of phase oscillators have been studied in a number of papers [Ermentrout, 1985;Daido, 1988;Strogatz & Mirollo, 1988;Sakaguchi et al, 1988;Niebur et al, 1991]. The other case is that of a chain consisting of multistable units when the amplitude dynamics drastically affects and regulates the phase dynamics and vice versa [Defontaines et al, 1990; Φ χ 1 −π π Nekorkin et al, 1996Nekorkin et al, , 1997Nekorkin et al, , 1998Nekorkin et al, , 1999Sepulchre & MacKay, 1997] or each unit is a chaotic oscillator [Heagy et al, 1994;Dolnik & Epstein 1996;Huerta et al, 1998]. Multistable systems with rather strong noise intensity can exhibit stochastic resonance [Wiesenfeld & Jaramillo, 1998].…”