Enrique Peacock-López | PubMed Health

PubMed2006

Chemical oscillations and Turing patterns in a generalized two-variable model of chemical self-replication.

Chemical self-replication of oligonucleotides and helical peptides show the so-called square root rate law. Based on this rate we extend our previous work on ideal replicators to include the square root rate and other possible nonlinearities, which we couple with an enzimatic sink. Although the nonlinearity is necessary for complex dynamics, the nature of the sink is the essential feature in the mechanism that allows temporal and spatial patterns. We obtain exact general relations for the Poincare-Adronov-Hopf and Turing bifurcations, and our generalized results include the Higgins, autocatalator, and templator models as specific cases.

Journal Article↗

PubMed2005

Complex dynamics in a three-level trophic system with intraspecies interaction.

In this paper, we present a three-level trophic food chain, including intraspecies interaction. In contrast with other analyses, we consider the effect on the third trophic level by the first-level parameters. The model shows complex, as well as, chaotic oscillations. Bifurcation diagrams show period doubling route to chaos and crises. Also from the forward and backwards sections of the bifurcation diagrams, we find hysteresis. This result implies the coexistence of attractors for the same parameter values. In particular, we consider the coexistence of a chaotic and a P1 attractors. Our results show that the regulation in the food chain is not exclusive to either a food-prey or prey-predator interaction, but to a more subtle food-prey-predator interaction, where, for some parameter values, a food-prey or a prey-predator regulation may dominate the system's dynamics. Finally, we consider the impact of the intraspecies interaction in the overall dynamics of the food chain.

Animals↗