RETRACTED: New applications of Schrödinger type inequalities to the existence and uniqueness of Schrödingerean equilibrium
The authors consider the delayed Schrödingerean tritropic Hastings Powell model in dimensionless form given by \[ \frac{dx}{dt} \leq x(1-x)- \frac{a_1x}{1+b_1x}[y(t- \tau _1)], \] \[ \frac{dy}{dt} \leq -d_1y+ \frac{a_1x}{1+b_1x}y -\frac{a_2x}{1+b_2x}[z(t- \tau _2)], \] \[ \frac{dz}{dt} \leq -d_2z+ \frac{a_2x}{1+b_2x}z, \] where \(x,~y\) and \(z\) represent dimensionless population variables; \(t\) represents a dimensionless time variable and all of the parameters \(a_i,~b_i,~d_i~(i=1,2)\) are positive; \(\tau _1\) and \(\tau _2\) represent the period of prey transitioned to predator and predator transitioned to top predator, respectively. It must be noted that they have taken two different time delays. They introduce 5 non-negative equilibrium points of the system and give criteria when the Schrödinger equilibrium is locally asymptotically stable. Further they study the existence of Schrödinger Hopf bifurcation and investigated their stability and its direction.
Schrödingerean equilibrium, Schrödingerean Hopf bifurcation
scientific article; zbMATH DE number 6697299