Chemical reaction Lotka-Volterra mechanism

Lotka-Volterra mechanism A simple chemical reaction mechanism proposed as a possible mechanism of oscillating reactions. The process involves a conversion of a reactant R into a product P. The reactant flows into the reaction chamber at a constant rate and the product is removed at a constant rate, i.e. the reaction is in a steady state (but not in chemical equilibrium). The mechanism involves three steps ... 

Autocatalysis is involved in the first two steps of this process. It appears that oscillating chemical reactions have mechanisms that are different from the Lotka-Volterra mechanism. This type of mechanism does occur in certain types of complex system such as predator-prey relationships in biology. It was in the biological context that the mechanism was investigated by the Italian mathematician Vito Volterra (1860-1940). 

The known mechanisms that produce oscillatory behavior have two characteristics in common. The first is autocatalysis. The product of a step must catalyze that step, as in steps 1 and 2 of the Lotka-Volterra mechanism. The second is that nonlinear differential equations occur. That is, the variables must occur with powers greater than unity or as products. A mechanism has been proposed for the BZ reaction that has 18 steps and involves 21 different chemical species. A computer simulation of the 18 simultaneous rate differential equations for the mechanism has been carried out and does produce oscillatory behavior. It also exhibits the interesting behavior that all curves in phase space corresponding to different initial states eventually approach... 

Autocatalysis can cause sustained oscillations in batch systems. This idea originally met with skepticism. Some chemists believed that sustained oscillations would violate the second law of thermodynamics, but this is not true. Oscillating batch systems certainly exist, although they must have some external energy source or else the oscillations will eventually subside. An important example of an oscillating system is the circadian rhythm in animals. A simple model of a chemical oscillator, called the Lotka-Volterra reaction, has the assumed mechanism ... 

This feedback-type behavior has been first considered in the domain of mathematics, with explicit targeting chemistry. In 1910. Alfred Lotka proposed some differential equations that corresponded to the kinetics of an autocatalytic chemical reaction, and then with lto Volterra derived a differential equation that describes a general feedback mechanism (oscillations) known as the Lotka-Volterra model. However, chemistry has not been ready yet for this link. 

Now the question is how to construct the simplest model of a chemical oscillator, in particular, a catalytic oscillator. It is quite easy to include an autocatalytic reaction in the adsorption mechanism, for example A+B—> 2 A. The presence of an autocatalytic reaction is a typical feature of the known Bmsselator and Oregonator models that have been studied since the 1970s. Autocatalytic processes can be compared with biological processes, in which species are able to give birth to similar species. Autocatalytic models resemble the famous Lotka-Volterra equations (Berryman, 1992 Valentinuzzi and Kohen, 2013), also known as the predator-prey or parasite-host equations. 

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