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Complex Balanced Equilibria of Weakly Reversible Poly-PL Kinetic Systems and Evolutionary Games

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Mendoza,  Eduardo R.
Oesterhelt, Dieter / Membrane Biochemistry, Max Planck Institute of Biochemistry, Max Planck Society;

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Citation

Talabis, D. A. S. J., Magpantay, D. M., Mendoza, E. R., Nocon, E. G., & Jose, E. C. (2020). Complex Balanced Equilibria of Weakly Reversible Poly-PL Kinetic Systems and Evolutionary Games. MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 83(2), 375-402.


Cite as: http://hdl.handle.net/21.11116/0000-0006-72E1-B
Abstract
This study is concerned with chemical reaction networks endowed with poly-PL kinetics, that is, the positive linear combination of power law kinetic systems. We discovered that complex balanced equilibria exist for weakly reversible poly-PL kinetics with zero kinetic reactant deficiency. The result is then applied to evolutionary games with replicator dynamics such that the polynomial payoff functions lead to polynomial kinetic systems, a subset of poly-PL kinetic systems. In particular, sufficient conditions to admit a zero kinetic reactant deficiency were derived for games with nonlinear payoff functions and poly-PL kinetics, allowing the application of the main result.