The Application Of Biological Stoichiometry To The Discrete Biodynamics System

Biological stoichiometry is the study of the balance of energy and multiple chemical elements in biological systems. In the last decade, it has been introduced into biodynamics system and promoted new dynamic behaviors and insights. Loladze, et al (2004), by constructing continurous models, have testified that a stable equilibrium is possible with two predators on one prey, and offered an explanation for the phenomenons of coexistence or biodiversity in a sense, which is impossible in the opinion of the competitive exclusion principle (CEP). However, we note that continuous model itself mathematically preclude any possibility of chaos, but even one dimensional discrete systems can potentially exhibit it. In addition, the data for experiments are collected on discrete time intervals and many species have no over-lap whatsoever between successive generations. All these call for discrete model. We will construct the analogical discrete model, by capturing two essential elements C and P, investigate how the food quality effects the system. The paper will show that not only the coexistence is possible for two predators on one prey, but more intriguing and profound scenario can occur in the discrete model, such as through the periodic doubling route to chaos if the parameters chosen suitably. We hope that the theoretic analysis can offer a little help to mankind to understand, study, protect and maintain biodiversity, as far as in our lies.