The Ginzburg-Landau approach to oscillatory media

Chimera States in Continuous Media: Existence and Distinctness

The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises the question of whether an analogous phenomenon can occur in continuous media. Here, we show that chimera states can exist in continuous systems even when the coupling is strictly local, as in many fluid and pattern forming media. Using the complex Ginzburg-Landau equation as a model system, we characterize chimera states consisting of a coherent domain of a frozen spiral structure and an incoherent domain of amplitude turbulence. We show that in this case, in contrast with discrete network systems, fluctuations in the local coupling field play a crucial role in limiting the coherent regions. We suggest these findings shed light on new possible forms of coexisting order and disorder in fluid systems.

Experimental studies on long-wavelength instability and spiral breakup in a reaction-diffusion system

We investigate the behavior of spiral waves in a quasi-two-dimensional spatial open reactor using Belousov-Zhabotinsky reaction. The goal of this study is to answer two questions raised recently: Can a system sustain a stable long-wavelength modulated spiral? What causes the transition from spiral to defect-mediated turbulence? Our experimental results show that in a certain range of control parameters, a sustained long-wavelength modulated spiral is stable. The amplitude and the wavelength of modulations increase with the control parameter. As the latter is increased to across a threshold, defects are generated far away from the spiral center as a result of the neighboring two wave fronts being too close.

Emergent global oscillations in heterogeneous excitable media: the example of pancreatic beta cells

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled, despite the absence of a pacemaker region.

Nonlinear waves, patterns and spatio-temporal chaos in cellular neural networks

Spatio-temporal pattern formation occurring in discretely coupled nonlinear dynamical systems has been studied numerically. In this paper, we review the possibilities of using arrays of discretely coupled nonlinear electronic circuits to study these systems. Spiral wave initiation and Turing pattern formation are some of the examples. Sidewall forcing of Turing patterns is shown to be capable of driving the system into a perfect spatial organization, namely, a rhombic pattern, where no defects occur. The dynamics of the two layers supporting Turing and Hopf modes, respectively, is analysed as a function of the coupling strength between them. The competition between these two modes is shown to increase with the diffusion between layers. As well, the coexistence of low- and high-dimensional spatio-temporal chaos is shown to occur in one-dimensional arrays.

Parametric stimulation of hemopoietic stem cells in normals and in certain leukemias

The paper discusses certain distributive and clustering modes of stimulus P and of its receptors. When combined with topologic features peculiar to sources and stem cells, these parameters account not only for the cycling variations typical of normal stem cells but also for seemingly paradoxical shifts in proliferative activity of cells grafted into patients with chronic myeloid leukemias.