Spatial Patterns for Discrete Models of Diffusion in Excitable Media

Greenberg, J. M.; Hastings, S. P.

doi:10.1137/0134040

Cited by 317 publications

(170 citation statements)

References 9 publications

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“…The cycle allows recurrent spatial waves to propagate with a fixed period, T. For the syphilis parameters (see figure legend 2), Tz10 years, as observed in US syphilis datasets (see CDC 1997-to date; Girvan et al 2002). Similar spatial wave patterns had been observed in a number of biological contexts including epidemiology (Grenfell et al 2001), ecology (Blasius et al 1999), neural networks (Lewis & Rinzel 2000) and theoretical studies of excitable systems (Greenberg & Hastings 1978). We refer to a 'pacemaker' as a recurring concentric wave in the two-dimensional population space.…”

Section: Recurrent Circular Waves and Pacemaker Centresmentioning

confidence: 72%

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Litvak-Hinenzon

Stone

2008

J. R. Soc. Interface.

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The success of an infectious disease to invade a population is strongly controlled by the population's specific connectivity structure. Here, a network model is presented as an aid in understanding the role of social behaviour and heterogeneous connectivity in determining the spatio-temporal patterns of disease dynamics. We explore the controversial origins of longterm recurrent oscillations believed to be characteristic of diseases that have a period of temporary immunity after infection. In particular, we focus on sexually transmitted diseases such as syphilis, where this controversy is currently under review. Although temporary immunity plays a key role, it is found that, in realistic small-world networks, the social and sexual behaviour of individuals also has a great influence in generating long-term cycles. The model generates circular waves of infection with unusual spatial dynamics that depend on focal areas that act as pacemakers in the population. Eradication of the disease can be efficiently achieved by eliminating the pacemakers with a targeted vaccination scheme. A simple difference equation model is derived, which captures the infection dynamics of the network model and gives insights into their origins and their eradication through vaccination. Illustrative videos may be found in the electronic supplementary material.

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Section: Recurrent Circular Waves and Pacemaker Centresmentioning

confidence: 72%

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Litvak-Hinenzon

Stone

2008

J. R. Soc. Interface.

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“…This corresponds to one of the several variants of the model proposed by Greenberg and Hastings [8]. It was initially designed to provide a simple explanation for the mechanisms underlying pattern formation in excitable media.…”

Section: The Modelmentioning

confidence: 99%

Intensity coding in two-dimensional excitable neural networks

Copelli

Kinouchi

2005

Physica A: Statistical Mechanics and its Applications

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In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective large dynamical range. Therefore the network transfer (gain) function (which is Hill or Stevens law-like) is an emergent property generated from a pool of small dynamical range cells, providing a basis for a "neural psychophysics". The growth of the dynamical range with the system size is approximately logarithmic, suggesting a functional role for electrical coupling. For a fixed number of neurons, the dynamical range displays a maximum as a function of the refractory period, which suggests experimental tests for the model. A biological application to ephaptic interactions in olfactory nerve fascicles is proposed.

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“…Thus, the large patch breaks up into small ones again, and each small patch starts growing until it becomes too large again, and so on. This is the equivalent of an excitable medium scenario with a refractory phase (Greenberg and Hastings 1978) obviously resulting in the well-known spatiotemporal pattern of traveling and interfering waves. Empty pores represent the excitable phase, metabolically active pores are the excited ones, and the refractory phase includes metabolically inactive but saturated pores.…”

Section: Coexistence and Persistencementioning

confidence: 99%

The Origin of Life: Chemical Evolution of a Metabolic System in a Mineral Honeycomb?

et al. 2009

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For the RNA-world hypothesis to be ecologically feasible, selection mechanisms acting on replicator communities need to be invoked and the corresponding scenarios of molecular evolution specified. Complementing our previous models of chemical evolution on mineral surfaces, in which selection was the consequence of the limited mobility of macromolecules attached to the surface, here we offer an alternative realization of prebiotic grouplevel selection: the physical encapsulation of local replicator communities into the pores of the mineral substrate. Based on cellular automaton simulations we argue that the effect of group selection in a mineral honeycomb could have been efficient enough to keep prebiotic ribozymes of different specificities and replication rates coexistent, and their metabolic cooperation protected from extensive molecular parasitism. We suggest that mutants of the mild parasites persistent in the metabolic system can acquire useful functions such as replicase activity or the production of membrane components, thus opening the way for the evolution of the first autonomous protocells on Earth.

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Spatial Patterns for Discrete Models of Diffusion in Excitable Media

Cited by 317 publications

References 9 publications

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Intensity coding in two-dimensional excitable neural networks

The Origin of Life: Chemical Evolution of a Metabolic System in a Mineral Honeycomb?

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