In this paper, by using the Beurling-Nevanlinna type inequality we obtain new results on the existence of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator. Meanwhile, the local stability of the Schrödingerean equilibrium and endemic equilibrium of the model are also discussed. We specially analyze the existence and stability of the Schrödingerean Hopf bifurcation...

A delayed three-species food chain system with two types of functional responses, Holling type and Beddington–DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, the properties of Hopf bifurcation ...

Taking the delay due to the latent period of computer viruses and the delay due to the period that the anti-virus software uses to clean the computer viruses as the bifurcation parameters, local Hopf bifurcation of an epidemic model over the Internet is studied. We discuss the existence of the Hopf bifurcation under four conditions: (1) τ1 > 0, τ2 = 0, (2) τ1 = 0, τ2 > 0, (3) τ1 = τ2 = τ > 0, a...

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, fold or Neimark-Sacker bifurcations occur, ...

We show the existence of a local solution to a Hamilton–Jacobi–Bellman (HJB) PDE around a critical point where the corresponding Hamiltonian ODE is not hyperbolic, i.e., it has eigenvalues on the imaginary axis. Such problems arise in nonlinear regulation, disturbance rejection, gain scheduling, and linear parameter varying control. The proof is based on an extension of the center manifold theo...

It is shown that the quotients of Kähler surfaces under free anti-holomorphic involutions have vanishing Seiberg-Witten invariants. Various vanishing theorems have played important roles in gauge theory. The first among them, due to S. K. Donaldson [2], states that the Donaldson invariants vanish for any smooth closed oriented 4-manifold X which decomposes to a connected sum X1#X2 with b2 (X1) ...

We develop a theory of tubular neighborhoods for the lower strata in manifold strati"ed spaces with two strata. In these topologically strati"ed spaces, manifold approximate "brations and teardrops play the role that "bre bundles and mapping cylinders play in smoothly strati"ed spaces. Applications include the classi"cation of neighborhood germs, a multiparameter isotopy extension theorem and a...