RETRACTED ARTICLE: New applications of Schr\xf6dinger type inequalities to the existence and uniqueness of Schr\xf6dingerean equilibrium

Jianjie Wang,Hugo Roncalver

doi:10.1186/s13660-017-1332-0

Abstract

As new applications of Schrödinger type inequalities appearing in Jiang (J. Inequal. Appl. 2016:247, 2016), we first investigate the existence and uniqueness of a Schrödingerean equilibrium. Next we propose a tritrophic Hastings-Powell model with two different Schrödingerean time delays. Finally, the stability and direction of the Schrödingerean Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem.

Highlights

A biological system is a nonlinear system, so it is still a public problem how to control the biological system balance
May and Odter introduced a general example of such a generalized model, that is to say, they investigated a three species model and the results show that the positive equilibrium is always locally stable when the system has two equal time delays
Two different Schrödinger delays are incorporated into Schrödingerean tritrophic Hastings-Powell (STHP) model which will be given in the following

Summary

Introduction

A biological system is a nonlinear system, so it is still a public problem how to control the biological system balance. There is much research on the stability of predator-prey system with time delays. May and Odter (see [ ]) introduced a general example of such a generalized model, that is to say, they investigated a three species model and the results show that the positive equilibrium is always locally stable when the system has two equal time delays.

Results

Conclusion