The paper studies the existence of generalized synchronization in complex networks, which consist of chaotic systems. When a part of modified nodes are chaotic, and the others have asymptotically stable equilibriums or orbital asymptotically stable periodic solutions, under certain conditions, the existence of generalized synchronization can be turned to the problem of contractive fixed point i...

In this study, asymptotic analysis of an HIV-1 epidemic model with distributed intracellular delays is proposed. One delay term represents the latent period which is the time when the target cells are contacted by the virus particles and the time the contacted cells become actively infected and the second delay term represents the virus production period which is the time when the new virions a...

A population of individuals is divided into groups. Individuals are recurrently randomly matched with individuals from their group to play a generic symmetric 2-player game. Deterministic interand intragroup dynamics are derived from a model of individual imitation within groups and individual migration between groups. Conditions are identified under which subsets (components) of the set of sta...

In this work, we introduce a new class of numerical schemes for rarefied gas dynamic problems described by collisional kinetic equations. The idea consists in reformulating the problem using a micro-macro decomposition and successively in solving the microscopic part by using asymptotically stable Monte Carlo methods. We consider two types of decompositions, the first leading to the Euler syste...

How can neural circuits maintain stable activity states when they are constantly being modified by Hebbian processes that are notorious for being unstable? A new synaptic plasticity mechanism is presented here that enables a neuron to obtain homeostasis of its firing rate over longer timescales while leaving the neuron free to exhibit fluctuating dynamics in response to external inputs. Mathema...

In this article we present a class of position control schemes for robot manipulators based on feedback of visual information processed through artificial neural networks. We exploit the approximation capabilities of neural networks to avoid the computation of the robot inverse kinematics as well as the inverse task space camera mapping which involves tedious calibration procedures. Our main st...

We present a numerical algorithm for computing Lyapunov functions for a class of strongly asymptotically stable nonlinear differential inclusions which includes switched systems and systems with uncertain parameters. The method relies on techniques from nonsmooth analysis and linear programming and leads to a piecewise affine Lyapunov function. We provide a thorough analysis of the method and p...

The dynamics of a general in-host model with intracellular delay is studied. The model can describe in vivo infections of HIV-I, HCV, and HBV. It can also be considered as a model for HTLV-I infection. We derive the basic reproduction number R0 for the viral infection, and establish that the global dynamics are completely determined by the values of R0. If R0 < or = 1, the infection-free equili...

We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals’ preferences are drawn randomly from a class of distributions allowing for both common and idiosyncratic components. In this context, as the market grows large, all Pareto efficient mechanisms—including top trading cycles, serial dictatorship, and their randomized variants—are asympto...

A general discrete juvenile-adult population model with time-dependent birth rate and nonlinear survivorship rates is studied. When breeding is continuous, it is shown that the model has a unique globally asymptotically stable positive equilibrium provided the net reproductive number is larger than one. If it is smaller than one, then the extinction equilibrium is globally asymptotically stable...