Connecting fast-slow systems and Conley index theory via transversality.
Consensus of a two-agent system with nonlinear dynamics and time-varying delay
To explore the impacts of time delay on nonlinear dynamics of consensus models, we incorporate time-varying delay into a two-agent system to study its long-time behaviors. By the classical 3/2 stability theory, we establish a sufficient condition for the system to experience unconditional consensus. Numerical examples show the effectiveness of the proposed protocols and present possible Hopf bifurcations when the time delay changes.
Consequences of the meromorphic equivalence of standard matrix differential equations.
In this article we investigate the question [of] how meromorphic differential equations can be simplified by meromorphic equivalence. In the case of equations of block size 1, which generalizes the case of distinct eigenvalues, we identify a class of equations which are simplest possible in the sense that they carry the smallest number of parameters whithin their equivalence classes. We also discuss conditions under which individual equations can be simplified. Particular attention is paid to the...
Constant invariant solutions of the Poincaré center-focus problem.
Constrained least squares methods for linear timevarying DAE systems.
Constructing the minimal differential relation with prescribed solutions
Construction of interval wavelet based on restricted variational principle and its application for solving differential equations.
Construction of second order linear differential equations with solutions of prescribed properties
Constructive solution of coupled second order delay differential equations with variable coefficients.
Contact Lie algebras of vector fields on the plane.
Continuability and estimates of solutions of (a(t)ψ(x)x')' + c(t)f(x) = 0
Continuability, boundedness, and convergence to zero of solutions of a perturbed nonlinear ordinary differential equation
Continuity of the non-convex play operator in the space of rectifiable curves
We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the -norm and to the -strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.
Continuous dependence of boundary value for semiinfinite interval ordinary differential equations.
Continuous dependence of inverse fundamental matrices of generalized linear ordinary differential equations on a parameter
The problem of continuous dependence for inverses of fundamental matrices in the case when uniform convergence is violated is presented here.
Continuous dependence of solutions of generalized linear ordinary differential equations on a parameter
We present here the problem of continuous dependence for generalized linear ordinary differential equations in the case when uniform convergence is violated. This work continues research of M. Ashordia (1993) and M. Tvrdý (2002).
Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses
In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.
Continuous dependence on a parameter of solutions of generalized differential equations
Continuous dependence on data for quasiautonomous nonlinear boundary value problems.
Continuous dependence on parameters of the fixed points set for some set-valued operators
In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.