Approximate methods for calculating the period of oscillations for the generalized Lienard's differential equation
Approximate solutions of the forced Duffing equation with mixed nonlinearities.
Approximation of periodic solutions of a system of periodic linear nonhomogeneous differential equations
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid....
Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems
In this work we will consider a class of second order perturbed Hamiltonian systems of the form , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained...
Asymptotic behavior of non-linear inhomogeneous differential equations via non-standard analysis. Part II. Some applications to higher order equations
Asymptotic behavior of -periodic solutions of singularly perturbed second-order differential equation
Asymptotic conditions for solving non-symmetric problems of third order nonlinear differential systems.
Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations.
Averaging in an ordinary differential equation.
Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation
The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed....
Behavior of forced asymmetric oscillators at resonance.
Bifurcation and total stability
Bifurcation for second-order Hamiltonian systems with periodic boundary conditions.
Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas [Book]
Bifurcation from Periodic Solutions in Functional Differential Equations.
Bifurcation of closed orbits from a limit cycle in
Bifurcation of periodic and chaotic solutions in discontinuous systems
Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...
Bifurcation of periodic solutions from inversion of stability of periodic O.D.E.'S.
Bifurcation of periodic solutions in a rotationally symmetric oscillation system.
Bifurcation of periodic solutions in differential inclusions
Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.