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Spirals in scalar reactiondiffusion equations
 Internat. J. Bifur. Chaos Appl. Sci. Engrg
, 1995
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SPATIAL NOISE STABILIZES PERIODIC WAVE PATTERNS IN OSCILLATORY SYSTEMS ON FINITE DOMAINS ∗
"... Abstract. Invasions in oscillatory systems generate in their wake spatiotemporal oscillations, consisting of either periodic wavetrains or irregular oscillations that appear to be spatiotemporal chaos. We have shown previously that when a finite domain, with zeroflux boundary conditions, has been f ..."
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Abstract. Invasions in oscillatory systems generate in their wake spatiotemporal oscillations, consisting of either periodic wavetrains or irregular oscillations that appear to be spatiotemporal chaos. We have shown previously that when a finite domain, with zeroflux boundary conditions, has been fully invaded, the spatiotemporal oscillations persist in the irregular case, but die out in a systematic way for periodic traveling waves. In this paper, we consider the effect of environmental inhomogeneities on this persistence. We use numerical simulations of several predatorprey systems to study the effect of random spatial variation of the kinetic parameters on the dieout of regular oscillations and the longtime persistence of irregular oscillations. We find no effect on the latter, but remarkably, a moderate spatial variation in parameters leads to the persistence of regular oscillations, via the formation of target patterns. In order to study this target pattern production analytically, we turn to λ–ω systems. Numerical simulations confirm analagous behavior in this generic oscillatory system. We then repeat this numerical study using piecewise linear spatial variation of parameters, rather than random variation, which also gives formation of target patterns under certain circumstances, which we discuss. We study this in detail by deriving an analytical approximation to the targets formed when the parameter λ0 varies in a simple, piecewise linear manner across the domain, using perturbation theory. We end by discussing the applications of our results in ecology and chemistry.
Chasing: A Mechanism for Resistance against Parasites in Selfreplicating Systems.
"... . We have performed calculations on two dimensional cellular automata models with cluster formation for various catalytic networks, especially a simple autocatalytic species and the hypercycle with few species. We discuss the mechanisms of cluster formation. A mechanism for resistance to parasites ..."
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. We have performed calculations on two dimensional cellular automata models with cluster formation for various catalytic networks, especially a simple autocatalytic species and the hypercycle with few species. We discuss the mechanisms of cluster formation. A mechanism for resistance to parasites is discovered for clusters with a single autocatalytic species and other networks giving essentially homogeneous clusters: As the parasite attacks a cluster from one side, the cluster may grow fast enough in the opposite direction to prevent destruction. Thus, the parasite will be chasing the main species in the cluster. As correlations and local effects are important for these results, they are expected to be obtained only in cellular automata and not in models based on partial differential equations. 1 Introduction Reactiondiffusion systems often lead to spatial patterns which appear for a large number of different applications [1, 2, 3, 4]. They have been studied frequently with many...
Harmonic Resonance Theory: An Alternative to the "Neuron Doctrine" Paradigm of Neurocomputation to Address Gestalt properties of perception
, 2000
"... neurocomputation involves discrete signals communicated along fixed transmission lines between discrete computational elements. This concept is shown to be inadequate to account for invariance in recognition, as well as for the holistic global aspects of perception identified by Gestalt theory. A Ha ..."
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neurocomputation involves discrete signals communicated along fixed transmission lines between discrete computational elements. This concept is shown to be inadequate to account for invariance in recognition, as well as for the holistic global aspects of perception identified by Gestalt theory. A Harmonic Resonance theory is presented as an alternative paradigm of neurocomputation, that exhibits both the property of invariance, and the emergent Gestalt properties of perception, not as special mechanisms contrived to achieve those properties, but as natural properties of the resonance itself.
The Electric Charge and Magnetization Distribution of the Nucleon: Evidence of a Subatomic Turing Wave Pattern
, 2008
"... Subquantum kinetics, a physics methodology that applies general systems theoretic concepts to the field of microphysics has gained the status of being a viable unified field theory. Earlier publications of this theory had proposed that a subatomic particle should consist of an electrostatic field th ..."
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Subquantum kinetics, a physics methodology that applies general systems theoretic concepts to the field of microphysics has gained the status of being a viable unified field theory. Earlier publications of this theory had proposed that a subatomic particle should consist of an electrostatic field that has the form of a radial Turing wave pattern whose form is maintained through the ongoing activity of a nonlinear reactiondiffusion medium that fills all space. This subatomic Turing wave prediction now finds confirmation in recent nucleon scattering form factor data which show that the nucleon core has a Gaussian charge density distribution with a peripheral periodicity whose wavelength approximates the particle's Compton wavelength and which declines in amplitude with increasing radial distance. The subquantum kinetics explanation for the origin of charge correctly anticipates the observation that the proton's charge density wave pattern is positively biased while the neutron's is not. The phenomenon of beta decay is interpreted as the onset of a secondary bifurcation leading from the uncharged neutron solution to the charged proton solution. The Turing wave dissipative structure prediction is able to account in a unitary fashion for nuclear binding, particle diffraction, and electron orbital quantization. The wave packet model is shown to be fundamentally flawed implying that quantum mechanics does not realistically represent the microphysical world. This new conception points to the possible existence of orbital energy states below the Balmer ground state whose transitions may be tapped as a new source of energy.