Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case.
Continuous dependence on parameters and boundedness of solutions to a hysteresis system
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.
Contractive mappings and periodically perturbed conservative systems
Contributions of Alan C. Lazer to mathematical population dynamics.
Convergence acceleration of shifted transformations for totally nonnegative Hessenberg matrices
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....
Correction to our paper “Periodic solutions to abstract differential equations”
Corrections to "Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas" (Dissertationes Math. 291 (1990))
Critical Point Theorems for Indefinite Functionals.
Die Eindeutigkeit des Grenzzyklus bei der Liénardschen Differentialgleichung.
Differential equations with infinite number of limit cycles
Distribution of zeros of solutions of certain periodic differential equations
Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities.
Double periodic solutions for a ratio-dependent predator-prey system with harvesting terms on time scales.
Duality mapping and the existence of periodic solutions for non-autonomous second order systems.
Dynamic analysis of an impulsively controlled predator-prey system.
Dynamical behavior of Volterra model with mutual interference concerning IPM
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...
Dynamical behavior of Volterra model with mutual interference concerning IPM
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...
Dynamical systems modelled by third order differential equations with special respect to the influence of the restoring term on the properties of solutions
Dynamical systems with newtonian type potentials
Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls
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.