We analyze an ordinary differential system with a hysteresis-relay nonlinearity in two cases when the system is autonomous or nonautonomous. Sufficient conditions for both the continuous dependence on the system parameters and the boundedness of the solutions to the system are obtained. We give a supporting example for the autonomous system.
We design shifted transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted transformations by considering the concept of the Newton shift....
A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...
A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...
This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.
In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.