Three-dimensional cooperative irreducible systems with a first integral
Time averaging for functional differential equations.
Time averaging for ordinary differential equations and retarded functional differential equations.
Time delay in chemical exchange during an NMR pulse
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all...
To conjugacy functions of second order linear differential equations
To existence of the periodic solution of a third-order nonlinear differential equation
To the definition of the global transformation in 2-dimensional linear spaces of continuous functions
To the question of oscillation of solutions of two-dimensional differential systems with deviated arguments.
To the theory of central dispersions for the linear differential equations of a finite type-special
To the theory of global transformation of the second order linear differential equations of finite type, special
Topogical equivalence of monotone nonlinear nonautonomous differential equations
Topological entropy and differential equations
On the background of a brief survey panorama of results on the topic in the title, one new theorem is presented concerning a positive topological entropy (i.e. topological chaos) for the impulsive differential equations on the Cartesian product of compact intervals, which is positively invariant under the composition of the associated Poincaré translation operator with a multivalued upper semicontinuous impulsive mapping.
Topological equivalence and topological linearization of controlled dynamical systems
Topologická klasifikácia diferenciálnych rovníc a štrukturálna stabilita
Total oscillatory behaviour globally in the delays
Totally bounded differential polynomial systems in
Totally bounded differential systems in are defined as having all trajectories bounded. By Dulac’s finiteness theorem it is proved that totally bounded polynomial systems exhibit an unbounded «annulus» of cycles. The portrait of the remaining trajectories is examined in the case the system has, in , a unique singular point. Work is in progress concerning the study of totally bounded polynomial systems with two singular points.
Tracking invariant manifolds without differential forms.
Tracking with prescribed transient behaviour
Universal tracking control is investigated in the context of a class of -input, -output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal of class (absolutely...
Tracking with prescribed transient behaviour
Universal tracking control is investigated in the context of a class S of M-input, M-output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal r of class W1,∞ (absolutely...
Trajectory sensitivity method and master-slave synchronization to estimate parameters of nonlinear systems.