Dynamics Of Producer-Consumer Models Based On Stoichiometry

The relationship between the consumer and the producer is extensive and important in ecosystems.Most researchers only focus on the energy flow between the consumer and the producer,but ignore the effect of nutrient elements on species dynamics.In most consumerproducer models,the growth of the producer is described by Logistic model,which is not suitable for describing the growth of the consumer in grassland ecosystem.Turchin has developed a Regrowth-Consumer model that describes the interactions between the vegetation and the rodent populations in grassland ecosystems.This work provides a concise framework for conusmer-producer relationship in grassland ecosystem.In this work,a stoichiometric consumer-producer model is established based on Turchin model by adding trophic dynamics.The analysis shows that the dynamic behavior of the model is richer than that of the traditional consumer-producer model.The results of dynamic analysis and numerical simulation showed that there was no limit cycle in the model.According to the solution curve of the model,the model can explain the paradox of enrichment and reflect the rapid growth of the vegetation.Finally,based on stoichiometric regrowth-consumer model,we established a stoichiometric regrowth-consumer model that consider the free phosphorus in the media.The model tracks free P in media and the consumer.The bifurcation diagram of the model shows that the dynamic behavior of the model is similar to that of the previous model,but the model can be easily extended to multiple the producer and the consumer.