This note discusses the interplay between dissipativity and asymptotics of continuous-time infinite-horizon optimal control problems. We focus on results convergence primal solutions derived in [6]. Moreover, we present a result attractivity adjoint trajectories, which is closely related to transversality conditions for Proofs further can be found

This paper infers from a generalized Picone identity the uniqueness of stable positive solution for class semilinear equations superlinear indefinite type, as well and global attractivity coexistence state in two diffusive prototypes symbiotic competing species models Lotka–Volterra. The optimality these theorems reveals tremendous strength identity.

Modelling land use dynamics is a critical scientific issue. Despite diversity of models coming from the fields remote sensing, geography, and economics, including multicriteria decision analysis machine-learning models, taking into account external driving factors urbanization still main challenge. This study aims at simulating various development scenarios with global local parameters. Thus, d...

We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability global attractivity its positive equilibrium are established. Our criteria depend on size some delays, improve results in recent literature provide answers to open problems.

Mammalian newborns exhibit avid responsiveness to odor compounds emanating from conspecific milk. Milk is however developmentally heterogeneous in composition as a function of both evolved constraints and offspring demand. The present study aimed to verify whether milk odor attractivity for neonates is equally distributed along lactation in Mus musculus (Balb-c strain). Therefore, we exposed pu...

This paper studies problems such as: given a discrete time dynamical system of the form x(t + 1) = f(x(t)) where f : R → R is a (possibly discontinuous) piecewise affine function, decide whether all trajectories converge to 0. We show in our main theorem (Theorem 2) that this Attractivity Problem is undecidable as soon as n ≥ 2. The same is true of two related problems: Stability (is the dynami...