Construction of a smooth Lyapunov function for an asymptotically stable set
Construction of Lyapunov functionals for linear Volterra integrodifferential equations and stability of delay systems.
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 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...
Correction and addition to my paper “The normal form and the stability of solutions of a system of differential equations in the complex domain”
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.
Decentralized control and synchronization of time-varying complex dynamical network
A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller...
Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch
A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the...
Delay-dependent asymptotic stability for neural networks with time-varying delays.
Description of a class of multivalued differential equations with almost weakly stable trivial solution
Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions in a rational functional form approximating a maximal Lyapunov function that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions for a class of hybrid (piecewise...
Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model
An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling...
Differential conditions to verify the Jacobian Conjecture
Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
Differential inequalities with initial time difference and applications.
Discontinuous Liapunov functions for differential equations with measurable right-hand sides