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      Autowave processes in a distributed chemical system.

      Journal of Theoretical Biology
      Arrhythmias, Cardiac, Biological Evolution, Bromates, Diffusion, Malonates, Memory, Short-Term, Models, Chemical, Morphogenesis, Periodicity

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          Impulses and Physiological States in Theoretical Models of Nerve Membrane

          Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model" has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a "physiological state diagram," with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.
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            Concentration wave propagation in two-dimensional liquid-phase self-oscillating system.

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              On Symmetry‐Breaking Instabilities in Dissipative Systems

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                Author and article information

                Journal
                4723554
                10.1016/0022-5193(73)90164-1

                Chemistry
                Arrhythmias, Cardiac,Biological Evolution,Bromates,Diffusion,Malonates,Memory, Short-Term,Models, Chemical,Morphogenesis,Periodicity

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