Autocatalytic reactions as dynamical systems on the interval

1993 ◽  
Vol 34 (11) ◽  
pp. 5238-5251 ◽  
Author(s):  
Lamberto Rondoni
Keyword(s):  
Dynamical Systems ◽  
Autocatalytic Reactions

scholarly journals Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators

1997 ◽  
Vol 1 (2) ◽  
pp. 161-167 ◽  
Author(s):  
Gerold Baier ◽  
Sven Sahle
Keyword(s):  
Dynamical Systems ◽  
Finite Number ◽  
Temporal Patterns ◽  
Autocatalytic Reaction ◽  
Living Systems ◽  
First Order ◽  
Autocatalytic Reactions ◽  
Complex Patterns ◽  
Spatio Temporal

We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a) a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b) a minimal two-variable oscillator with one first-order autocatalytic reaction; (c) a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.

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