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1988 (2)
1984 (1)
1Author    Igor Schreiber, Milan Kubíček, M. Iloš MarekRequires cookie*
 Title    Impaired Diffusion Coupling-Source of Arrhythmia in Cell Systems  
 Abstract    A detailed analytical and numerical analysis of a simple reaction-diffusion model of the source of non-homogeneities and arrhythmias in an originally homogeneous reaction system is pre­ sented. Solution, bifurcation and evolution diagrams are used to describe the behaviour of the model. It is shown that under certain conditions steady and/or oscillatory nonhomogeneous states are the only stable solutions of the model. These phenomena are essentially not dependent on a particular reaction kinetics. A possible relevance to some biological situations is discussed. 
  Reference    Z. Naturforsch. 39c, 1170—1179 (1984); received December 3 1982/May 16 1984 
  Published    1984 
  Keywords    Reaction-Diffusion Systems, Dissipative Structures, Oscillations, Synchronization, Arrhythmias 
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 TEI-XML for    default:Reihe_C/39/ZNC-1984-39c-1170.pdf 
 Identifier    ZNC-1984-39c-1170 
 Volume    39 
2Author    Gerold Baier, Peter Urban, Klaus WegmannRequires cookie*
 Abstract    N e w M o d e l S y s te m fo r th e S tu d y o f C o m p le x D y n a m ic a l E n z y m e R e a c tio n s . I. A N o n lin e a r E n z y m e R e a c tio n in a C h e m ic a l G r a d ie n t An experimental system for the study of biochemical reaction dynamics is introduced and de­ scribed. A one-enzyme reaction is extended by an artificial feedback loop in an electrochemical device. Cyclic voltammetry is used to show that the reaction rate depends nonlinearly on the amount of cosubstrate offered. For some sets of fixed parameter values a damped oscillatory approach of the steady state was observed. The usefulness of the systems theoretical concepts is discussed. 
  Reference    Z. Naturforsch. 43a, 987—994 (1988); Received August 22 1988 
  Published    1988 
  Keywords    Reaction-diffusion Systems, Peroxidase, Feedback, Nonlinearity, Damped Oscillations 
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 TEI-XML for    default:Reihe_A/43/ZNA-1988-43a-0987.pdf 
 Identifier    ZNA-1988-43a-0987 
 Volume    43 
3Author    Georg Purwins, Christian Radehaus, Jürgen BerkemeierRequires cookie*
 Title    Hans  
 Abstract    We investigate experimentally stationary stable states of activator (w) inhibitor (v) type systems corresponding to the reaction diffusion equation S ■ v = Av + w — v; w = a Aw + f(w) — v; S, a — const > 0 with / (w) monotonically increasing for small and decreasing for large |w|. We first describe some general mathematical properties and present qualitative results obtained from numerical calcula­ tions. We then investigate experimentally electrical networks described by the spatially discretized version of the above equation. Calculation and experiment are in good agreement. We also interprete a two dimensional-network as an equivalent circuit for a composite material consisting of a linear and a nonlinear layer with an s-shaped current density electric field characteristic. This model is used for a phenomenological description of spatial structures and global current voltage characteristics observed experimentally in pin-diode like and gas discharge devices. The model accounts very well for the experimental results obtained so far. It is concluded that the above equation and the corresponding experimental setup are of great interest for fundamental investigations of self con­ trolled processes in nature. E x p e r im e n ta l I n v e s tig a tio n o f S p a t ia l P a t t e r n F o r m a tio n in P h y s ic a l S y s te m s o f A c tiv a to r I n h ib ito r T y p e 
  Reference    Z. Naturforsch. 43a, 17—29 (1988); received October 10 1987 
  Published    1988 
  Keywords    Activator Inhibitor System, Reaction Diffusion System, Electrical Network, Semicon­ ductor, Gas Discharge 
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 TEI-XML for    default:Reihe_A/43/ZNA-1988-43a-0017.pdf 
 Identifier    ZNA-1988-43a-0017 
 Volume    43