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1999 (1)
1978 (1)
1Author    Masayasu Mimura, J. D. MurrayRequires cookie*
 Title    Spatial Structures in a Model Substrate-Inhibition Reaction Diffusion System  
 Abstract    An important new model universal oscillator proposed by Seelig which depends on substrate inhibition is considered. In a finite spatial domain with zero flux boundary conditions and in which the substrates can diffuse it is shown that diffusion-driven instability is possible and can result in finite amplitude spatial structures. Illustrative numerical results are presented which exhibit this behaviour. 
  Reference    Z. Naturforsch. 33c, 580 (1978); received M ay 18 1978 
  Published    1978 
  Keywords    Reaction-Diffusion, Spatial Pattern, Substrate Inhibition 
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 TEI-XML for    default:Reihe_C/33/ZNC-1978-33c-0580.pdf 
 Identifier    ZNC-1978-33c-0580 
 Volume    33 
2Author    J. Ackermann, T. KirnerRequires cookie*
 Title    Parasites and Pattern Formation  
 Abstract    Biological information is coded in replicating molecules. To maintain a given amount of in-formation a cooperative interaction between these molecules is essential. The main problem for the stability of a system of prebiotic replicators are emerging parasites. Stabilization against such parasites is possible if space is introduced in the model. Complex patterns like spiral waves and self-replicating spot patterns have been shown to stabilize such systems. Stability of replicating systems, however, occurs only in parameter regions were such complex patterns occur. We show that parasites are able to push such systems into a parameter region were life is possible. To demonstrate this influence of parasites on such systems, we introduce a parasitic species in the Gray-Scott model. The growing concentration of parasites will kill the system, and the cooperative Gray-Scott system will be diluted out in a well mixed flow reactor. While considering space, in the model stabilizing pattern formation in a narrow parameter region is possible. We demonstrate that the concentration of the parasitic species is able to push the system into a region were stabilizing patterns emerge. 
  Reference    Z. Naturforsch. 54a, 146—152 (1999); received December 15 1998 
  Published    1999 
  Keywords    Pattern Formation, Reaction-Diffusion, Molecular Evolution, Parasites, Coevolution, Cooperation 
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 TEI-XML for    default:Reihe_A/54/ZNA-1999-54a-0146.pdf 
 Identifier    ZNA-1999-54a-0146 
 Volume    54