A converse Lyapunov theorem and robustness with respect to unbounded perturbations for exponential dissipativity.
A discrete Lyapunov theorem for the exponential stability of evolution families.
A General Cooperation Theorem for Hypercycles.
A Lyapunov function for pullback attractors of nonautonomous differential equations.
A necessary and sufficient condition for stability of the convex combination of polynomials
A note on bounded, periodic and stable solutions of differential equations
A Note on Multistep Methods and Attracting Sets of Dynamical Systems.
A note on stability properties of integrated semigroups
A note on the asymptotic stability in the whole of non-autonomous systems.
A Note on the Covergence of Solutions of a System of Differential Equations. (Short Communication).
A Note on the Covergence of Solutions of a System of Differential Equations.
A note on the Perron instability theorem.
A predator-prey model with state dependent impulsive effects
We investigate a Lotka-Volterra predator-prey model with state dependent impulsive effects, in which the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. We present some sufficient conditions to guarantee the existence and asymptotical stability of semi-trivial periodic solutions and positive periodic solutions.
A prey-predator model with a cover linearly varying with the prey population and an alternative food for the predator.
A simple boundedness theorem for a Liénard equation with damping
A simple model of thermoelectric oscillations
A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
A smooth Lyapunov function from a class- estimate involving two positive semidefinite functions
A smooth Lyapunov function from a class- estimate involving two positive semidefinite functions
We consider differential inclusions where a positive semidefinite function of the solutions satisfies a class- estimate in terms of time and a second positive semidefinite function of the initial condition. We show that a smooth converse Lyapunov function, i.e., one whose derivative along solutions can be used to establish the class- estimate, exists if and only if the class- estimate is robust, i.e., it holds for a larger, perturbed differential inclusion. It remains an open question whether...
A solution of the continuous Lyapunov equation by means of power series
A solution to the bidimensional global asymptotic stability conjecture