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- Yuliya N. Kyrychko, Stephen A. Gourley, Michele Bartuccelli
- SIAM J. Math. Analysis
- 2006

In this paper we derive a stage-structured model for a single species on a finite one-dimensional lattice. There is no migration into or from the lattice. The resulting system of equations, to be solved for the total adult population on each patch, is a system of delay equations involving the maturation delay for the species, and the delay term is nonlocal… (More)

- Michele Bartuccelli, J. H. B. Deane, Guido Gentile, Stephen A. Gourley
- Applied Mathematics and Computation
- 2004

We consider a parametrically-driven nonlinear ODE, which encompasses a simple model of an electronic circuit known as a parametric amplifier, whose linearisation has a zero eigenvalue. By adopting two different approaches, we obtain conditions for the origin to be a global attractor which is approached (a) non-monotonically and (b) monotonically. In case… (More)

We consider a model for the injection-locked frequency divider, and study analytically the locking onto rational multiples of the driving frequency. We provide explicit formulae for the width of the plateaux appearing in the devil's staircase structure of the lockings, and in particular show that the largest plateaux correspond to even integer values for… (More)

We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasiperiodic analytic forcing term and in the presence of damping. As a physical application one can think of a resistor– inductor–varactor circuit with a periodic ͑or quasiperiodic͒ forcing function, even if the range of applicability of the… (More)

We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasiperiodic forcing term and in the presence of damping. In the limit of large damping, under some generic nondegeneracy condition on the force, there are quasiperiodic solutions which have the same frequency vector as the forcing term. We prove that… (More)

In this paper we investigate the conditions under which periodic solutions of the nonlinear oscillator¨x + x 3 = 0 persist when the differential equation is perturbed so as to becomë x + x 3 + εx 3 cos t + γ ˙ x = 0. For any frequency ω, there exists a threshold for the damping coefficient γ, above which there is no periodic orbit with period 2π/ω. We… (More)

We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction. We find that, if the damping coefficient increases in time up to a final… (More)

In this paper we investigate the conditions under which periodic solutions of the nonlinear oscillator¨x + x 3 = 0 persist when the differential equation is perturbed so as to becomë x + x 3 + εx 3 cos t + γ ˙ x = 0. We conjecture that for any periodic orbit, characterized by its frequency ω, there exists a threshold for the damping coefficient γ, above… (More)

We give a proof of the persistence of invariant tori for analytic perturbations of isochronous systems by using the Lindstedt series expansion for the solutions. With respect to the case of anisochronous systems, there is the additional problem to find the set of allowed rotation vectors for the invariant tori, which can not given a priori simply by looking… (More)

We study perturbations of a class of analytic two-dimensional autonomous systems with perturbations depending periodically on time; for instance one can imagine a periodically driven or forced system with one degree of freedom. In the first part of the paper, we revisit a problem considered by Chow and Hale on the existence of subharmonic solutions. In the… (More)