Existence problems for -closed orbits.
Fast and heteroclinic solutions for a second order ODE.
First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems.
From transverse heteroclinic cycles to transverse homoclinic orbits
Generalized linking theorem and nonlinear equations in unbounded domains
Global bifurcations in a dynamical model of recurrent neural networks
The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves...
Global homoclinic bifurcation for damped systems.
Heteroclinic connections for a class of non-autonomous systems.
Heteroclinic orbits in plane dynamical systems
We consider general second order boundary value problems on the whole line of the type , , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the plane dynamical system.
Heteroclinic solutions to an asymptotically autonomous second-order equation.
Heteroclinics for a class of fourth order conservative differential equations
Higher-order Melnikov functions for single-DOF mechanical oscillators: theoretical treatment and applications.
Homoclinic and period-doubling bifurcations for damped systems
Homoclinic and periodic solutions of scalar differential delay equations
Homoclinic orbits for a class of infinite dimensional hamiltonian systems
Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
Homoclinic orbits for a class of symmetric Hamiltonian systems.
Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³
This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.
Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
Homoclinic solutions for a class of second order non-autonomous systems.