COMPETITIVE SYSTEMS AND ORBITAL STABILITY IN R RAFAEL ORTEGA AND LUIS ÁNGEL SÁNCHEZ (Communicated by Hal L. Smith) Abstract. Competitive autonomous systems in R3 have the remarkable property of verifying an analogue of the Poincaré-Bendixon theorem for planar equations. This fact allows us to prove the existence of orbitally stable closed orbits for those systems under easily checkable hypothes...

In this work we develop some aspects of the theory of Hopf algebras to the context of autonomous map pseudomonoids. We concentrate in the Hopf modules and the Centre or Drinfel’d double. If A is a map pseudomonoid in a monoidal bicategory M , the analogue of the category of Hopf modules for A is an Eilenberg-Moore construction for a certain monad in Hom(M op,Cat). We study the existence of the ...

In this paper, we investigate consensus and disturbance attenuation in a chain of mobile agents, which include non-autonomous agents, semi-autonomous agents and autonomous agents. In particular, the nonlinear dynamics of non-autonomous agents is given and cannot be designed, while the dynamics of semi-autonomous and autonomous agents can be partially and fully designed, respectively. To improve...

In this paper, we consider the time minimal problem for an Autonomous Underwater Vehicle. We investigate, on a simplified model, the existence of singular extremals and discuss their optimality status. Moreover, we prove that singular extremals corresponding to the angular acceleration are of order 2. We produce in this case a semicanonical form of our Hamiltonian system and we can conclude the...

This paper addresses the global existence and global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays. By using a novel approach, sufficient conditions are derived for the existence and global exponential convergence of positive solutions of the model without any restriction on uniform positiveness of the per capita dead rate. Numerical exam...

This paper studies the existence of periodic solutions to the delay differential equation ẋ(t) = f(x(t− μτ(t)), ) . The analysis is based on a perturbation method previously used for retarded differential equations with constant delay. By transforming the studied equation into a perturbed non-autonomous ordinary equation and using a bifurcation result and the Poincaré procedure for this last eq...