A contribution to the theory of stability of differential equations in Banach space
A converse Lyapunov theorem and robustness with respect to unbounded perturbations for exponential dissipativity.
A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension
In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.
A note on linear perturbations of oscillatory second order differential equations
Under suitable hypotheses on , , we prove some stability results which relate the asymptotic behavior of the solutions of to the asymptotic behavior of the solutions of .
A note on the fundamental matrix of variational equations in
The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in . An application concerning computation of a derivative of a scalar Poincaré mapping is given.
A partial generalization of Diliberto’s theorem for certain DEs of higher dimension
A proof existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems.
A remark on the half-linear extension of the Hartman-Wintner theorem.
A stability theory for perturbed differential equations.
An extension of Milloux's theorem to half-linear differential equations.
Analysis of Synchronization in a Neural Population by a Population Density Approach
In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate...
Approximation of analytic functions by Kummer functions.
Approximation of limit cycle of differential systems with variable coefficients
The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.
Asymptotic behavior of the solutions to a class of second-order differential systems.
Asymptotic relationship between solutions of two systems of differential equations
Bemerkungen zu Stabilitätsfragen für verallgemeinerte Differentialgleichungen
Bifurcation of closed orbits from a limit cycle in
Bifurcation of multi-bump homoclinics in systems with normal and slow variables.
Boundary value problems for doubly perturbed first order ordinary differential systems.
Bounded solutions to perturbed nonlinear systems and asymptotic relationships.