The role of delay in digestion of plankton by fish population: A fishery model.
The role of the incubation period in a disease model.
The stability of Nash-Cournot equilibria in labor managed oligopolies.
The steepest descent dynamical system with control. Applications to constrained minimization
Let be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [5]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with and a control...
The steepest descent dynamical system with control. Applications to constrained minimization
Let H be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint S. A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [CITE]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with S and...
The study of the chaotic behavior in retailer's demand model.
The uniform attractors for the nonhomogeneous 2D Navier-Stokes equations in some unbounded domain.
Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems.
Theory of adaptive adjustment.
Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems.
Time in dynamical systems.
Time to the convergence of evolution in the space of population states
Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation...
Topological entropy of Cournot-Puu duopoly.
Towards a theory of mind.
Toy quantum mechanics using hidden variables.
Traveling front solutions for a diffusive epidemic model with external sources
Triple Collision in the Collinear Three-Body Problem.
Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem
This paper presents a new robust adaptive model predictive control for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound, as well as constraints on input states. An adaptive control is used in the new controller to estimate the system uncertainty. Also, to avoid the system disturbances, a method is employed to find the appropriate gain in Tube-MPC. Finally, a surge avoidance problem in centrifugal compressors...
Tumour angiogenesis model with variable vessels' effectiveness
We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...