Contributions of Alan C. Lazer to mathematical population dynamics.
Contributions to the asymptotic behaviour of the equation with a complex-valued function
Control a state-dependent dynamic graph to a pre-specified structure
Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states....
Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems
This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this “weak” Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration.
Convergence of solutions for a fifth-order nonlinear differential equation.
Convergence of solutions of certain fourth-order nonlinear differential equations.
Convergence of solutions of certain non-homogeneous third order ordinary differential equations
Convergence of the solutions for the equation .
Converse theorem for practical stability of nonlinear impulsive systems and applications
The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of...
Convexity of the stability region of Hurwitz systems of differential equations.
Coppel-Conti sets of linear systems.
Correction and addition to my paper “The normal form and the stability of solutions of a system of differential equations in the complex domain”
Corrections to "Existence and stability of solutions for semilinear Dirichlet problems" (Ann. Polon. Math. 88 (2006), 127-139)
Critical case of multiple pairs of pure imaginary roots of a nonautonomous essentially nonlinear th-order equation.
Critical case of multiple pairs of pure imaginary roots of a nonautonomous essentially nonlinear differential system.