The first discrete Painlevé equation (dPI), which appears in a model of quantum gravity, is an integrable nonlinear nonautonomous difference equation which yields the well known first Painlevé equation (PI) in a continuum limit. The asymptotic study of its solutions as the discrete time-step n → ∞ is important both for physical application and for checking the accuracy of its role as a numerica...

It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and nonautonomous lattice equations. As results of this approach, we obtain new reductions of the discrete potential Kor...

Although numerous attempts have been made by various researchers to find a method to solve the general case, a successful technique remains elusive. For example, a paper by Caviglia and Morro [2] disproves an effort to do so using quadratures. The authors express the notion that such an achievement would be remarkable, but the ability to solve a first order homogeneous nonautonomous system usin...

This paper deals with a synthesis of a nonautonomous system with a stable limit cycle. By extending Green’s method, by which arbitrary periodic solutions can be designed in autonomous systems, it is shown that a nonautonomous system whose transient trajectories converge to a prescribed limit cycle can be synthesized. Furthermore, we apply receding horizon control to determine the optimal time-d...

With the aid of a direct projective approach, a general transformation solution for the nonautonomous nonlinear Schrödinger (NLS) system is derived. Based on certain known exact solutions of the projective equation, some periodic and localized excitations with novel properties are correspondingly revealed by entrancing appropriate system parameters. The integrable constraint conditions for the ...

a memory control for t-s fuzzy discrete-time systems with sto- chastic input delay is proposed in this paper. dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis- tribution. a new state space model of the discrete-time t-s fuzzy system is derived by introducing some stocha...

A nonautonomous semiratio-dependent predator-prey systemwith nonmonotonic functional responses is investigated. For general nonautonomous case, positive invariance, permanence, and globally asymptotic stability for the system are studied. For the periodic (almost periodic) case, sufficient conditions for existence, uniqueness, and stability of a positive periodic (almost periodic) solution are ...