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Monographie ausleihbar

Analysis and simulation of chaotic systems (1993)

Hoppensteadt, Frank C.

New York [u.a.] : Springer

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Signatur: AWI A17-94-0166

In: Applied mathematical sciences

Materialart: Monographie ausleihbar

Seiten: XVII, 305 S.

ISBN: 3540979166

Serie: Applied mathematical sciences 94

Zweigbibliothek: AWI Bibliothek

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Digitale Medien

Book reviews (1997)

Hoppensteadt, Frank ; Hastings, Harold M. ; Mesterton-Gibbons, Michael ; [weitere]

Springer

Bulletin of mathematical biology 59 (1997), S. 787-807

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ISSN: 1522-9602

Quelle: Springer Online Journal Archives 1860-2000

Thema: Biologie , Mathematik

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02458430

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3

Digitale Medien

Asymptotic series solutions of some nonlinear parabolic equations with a small parameter (1969)

Hoppensteadt, Frank

Springer

Archive for rational mechanics and analysis 35 (1969), S. 284-298

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ISSN: 1432-0673

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik , Physik

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00248163

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4

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Oscillatory models of the hippocampus: A study of spatio-temporal patterns of neural activity (1999)

Borisyuk, Roman ; Hoppensteadt, Frank

Springer

Biological cybernetics 81 (1999), S. 359-371

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ISSN: 1432-0770

Quelle: Springer Online Journal Archives 1860-2000

Thema: Biologie , Informatik , Physik

Notizen: Abstract. Spatial patterns of theta-rhythm activity in oscillatory models of the hippocampus are studied here using canonical models for both Hodgkin's class-1 and class-2 excitable neuronal systems. Dynamics of these models are studied in both the frequency domain, to determine phase-locking patterns, and in the time domain, to determine the amplitude responses resulting from phase-locking patterns. Computer simulations presented here demonstrate that phase deviations (timings) between inputs from the medial septum and the entorhinal cortex can create spatial patterns of theta-rhythm phase-locking. In this way, we show that the timing of inputs (not only their frequencies alone) can encode specific patterns of theta-rhythm activity. This study suggests new experiments to determine temporal and spatial synchronization.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s004220050568

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Synaptic organizations and dynamical properties of weakly connected neural oscillators (1996)

Hoppensteadt, Frank C. ; Izhikevich, Eugene M.

Springer

Biological cybernetics 75 (1996), S. 117-127

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ISSN: 1432-0770

Quelle: Springer Online Journal Archives 1860-2000

Thema: Biologie , Informatik , Physik

Notizen: Abstract. We study weakly connected networks of neural oscillators near multiple Andronov-Hopf bifurcation points. We analyze relationships between synaptic organizations (anatomy) of the networks and their dynamical properties (function). Our principal assumptions are: (1) Each neural oscillatorcomprises two populations of neurons: excitatory and inhibitory ones; (2) activity of each population of neurons is described by a scalar (one-dimensional) variable; (3) each neural oscillatoris near a nondegenerate supercritical Andronov-Hopf bifurcation point; (4) the synaptic connections between the neural oscillatorsare weak. All neural networks satisfying these hypotheses are governed by the same dynamical system, which we call the canonical model. Studying the canonical model shows that: (1) A neural oscillatorcan communicate only with those oscillators which have roughly the same natural frequency. That is, synaptic connections between a pair of oscillators having different natural frequencies are functionally insignificant. (2) Two neural oscillatorshaving the same natural frequencies might not communicate if the connections between them are from among a class of pathological synaptic configurations. In both cases the anatomical presence of synaptic connections between neural oscillators does not necessarily guarantee that the connections are functionally significant. (3) There can be substantial phase differences (time delays) between the neural oscillators, which result from the synaptic organization of the network, not from the transmission delays. Using the canonical model we can illustrate self-ignition and autonomous quiescence (oscillator death) phenomena. That is, a network of passive elements can exhibit active properties and vice versa. We also study how Dale's principle affects dynamics of the networks, in particular, the phase differences that the network can reproduce. We present a complete classification of all possible synaptic organizations from this point of view. The theory developed here casts some light on relations between synaptic organization and functional properties of oscillatory networks. The major advantage of our approach is that we obtain results about all networks of neural oscillators, including the real brain. The major drawback is that our findings are valid only when the brain operates near a critical regime, viz. for a multiple Andronov-Hopf bifurcation.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s004220050279

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Synaptic organizations and dynamical properties of weakly connected neural oscillators II. Learning phase information (1996)

Hoppensteadt, Frank C. ; Izhikevich, Eugene M.

Springer

Biological cybernetics 75 (1996), S. 129-135

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ISSN: 1432-0770

Quelle: Springer Online Journal Archives 1860-2000

Thema: Biologie , Informatik , Physik

Notizen: Abstract. This is the second of two articles devoted to analyzing the relationship between synaptic organizations (anatomy) and dynamical properties (function) of networks of neural oscillators near multiple supercritical Andronov-Hopf bifurcation points. Here we analyze learning processes in such networks. Regarding learning dynamics, we assume (1) learning is local (i.e. synaptic modification depends on pre- and postsynaptic neurons but not on others), (2) synapses modify slowly relative to characteristic neuron response times, (3) in the absence of either pre- or postsynaptic activity, the synapse weakens (forgets). Our major goal is to analyze all synaptic organizations of oscillatory neural networks that can memorize and retrieve phase information or time delays. We show that such networks have the following attributes: (1) the rate of synaptic plasticity connected with learning is determined locally by the presynaptic neurons, (2) the excitatory neurons must be long-axon relay neurons capable of forming distant connections with other excitatory and inhibitory neurons, (3) if inhibitory neurons have long axons, then the network can learn, passively forget and actively unlearn information adjusting synaptic plasticity rates.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s004220050280

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Analysis and computer simulation of accretion patterns in bacterial cultures (1994)

Chiu, Chichia ; Hoppensteadt, Frank C. ; Jäger, Willi

Springer

Journal of mathematical biology 32 (1994), S. 841-855

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ISSN: 1432-1416

Schlagwort(e): Mathematical models ; Pattern formation ; Numerical methods ; Computer simulation

Quelle: Springer Online Journal Archives 1860-2000

Thema: Biologie , Mathematik

Notizen: Abstract Patterned growth of bacteria created by interactions between the cells and moving gradients of nutrients and chemical buffers is observed frequently in laboratory experiments on agar pour plates. This has been investigated by several microbiologists and mathematicians usually focusing on some hysteretic mechanism, such as dependence of cell uptake kinetics on pH. We show here that a simpler mechanism, one based on cell torpor, can explain patterned growth. In particular, we suppose that the cell population comprises two subpopulations —one actively growing and the other inactive. Cells can switch between the two populations depending on the quality of their environment (nutrient availability, pH, etc.) We formulate here a model of this system, derive and analyze numerical schemes for solving it, and present several computer simulations of the system that illustrate various patterns formed. These compare favorably with observed experiments.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00168801

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8

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Response of a solutivory chain to a nutrient pulse (1994)

Hoppensteadt, Frank C. ; Johnson, Paul M.

Springer

Journal of mathematical biology 32 (1994), S. 865-867

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ISSN: 1432-1416

Schlagwort(e): Dynamical systems ; Microbial ecology

Quelle: Springer Online Journal Archives 1860-2000

Thema: Biologie , Mathematik

Notizen: Abstract A microbial community model is proposed that accounts for byproducts of one strain being nutrients for another and for cells passing in and out of states of torpor. It is shown that such models can sustain the propagation of a nutrient pulse as observed, for example, in methanogenesis.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00168803

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