First integrals for the Duffing-Van der Pol type oscillator.
First integrals for two linearly coupled nonlinear Duffing oscillators.
First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems.
First phases of the associated equation with parameters for the differential equation
Five limit cycles for a simple cubic system.
We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.
Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations
The paper deals with the quasi-linear ordinary differential equation with . We treat the case when is not necessarily monotone in its second argument and assume usual conditions on and . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano, [Acta...
Fixed points, periodic points, and coin-tossing sequences for mappings defined on two-dimensional cells.
Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states
This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about “(x,u)-flatness”...
Floquet theory for linear differential equations with meromorphic solutions.
Flots sur le tore et nombres de rotation
Fluctuation patterns and conditional reversibility in nonequilibrium systems
Fonctions de Mathieu et fonctions propres de l'oscillateur relativiste
Forced oscillation of second order nonlinear dynamic equations on time scales.
Forced oscillation of second-order half-linear dynamic equations on time scales.
Forced oscillation of second-order nonlinear dynamic equations on time scales.
Forced oscillation of third order nonlinear dynamic equations on time scales
Consider the third order nonlinear dynamic equation , (*) on a time scale which is unbounded above. The function f ∈ C(,) is assumed to satisfy xf(x) > 0 for x ≠ 0 and be nondecreasing. We study the oscillatory behaviour of solutions of (*). As an application, we find that the nonlinear difference equation , where α ≥ -1, γ > 0, c > 3, is oscillatory.
Forced oscillations of first order nonlinear neutral differential equations.
Forced superlinear oscillations via Picone's identity.
Form of general pointwise transformations of linear differential equations
Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.