We consider a planar differential system ˙ x = P (x, y), ˙ y = Q(x, y), where P and Q are C 1 functions in some open set U ⊆ R 2 , and ˙ = d dt. Let γ be a periodic orbit of the system in U. Let f (x, y) : U ⊆ R 2 → R be a C 1 function such that P (x, y) ∂f ∂x (x, y) + Q(x, y) ∂f ∂y (x, y) = k(x, y) f (x, y), where k(x, y) is a C 1 function in U and γ ⊆ {(x, y) | f (x, y) = 0}. We assume that i...

39 We shall give three ' criteria for the uniqueness of limit cycles of systems of Liellard type x '= a(y)-f3(y)F(x}, y '= -g(x}, examples are provided to illustrate our results.

We investigate the possibility that the large mixing of neutrinos is induced by their large coupling to a five-dimensional bulk neutrino. In the strong coupling limit the model is exactly soluble. It gives rise to an oscillation amplitude whose squared-mass difference is independent of the channel, thus making it impossible to explain both the solar and the atmospheric neutrino oscillations sim...

Separatrix cycles for a planar quadratic vector field are studied. The results obtained are used to show that in any bounded region of the plane a quadratic vector field has at most a finite number of limit cycles.

Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems, are extended to continuous piecewise– linear differential systems. Then we obtain new results on the existence and uniqueness of limit cycles for systems with three linearity zones and without symmetry. We also reprove existing results of systems with two linearity zones giving shorter and ...

and Applied Analysis 3 where g x ax O x 1 , m ≥ 2 system 1.8 is a generalized Liénard system . Stróżyna and Żoła̧dek 17 proved that this formal normal form can be achieved through an analytic change of variables. Thus, if 1.4 has a center or focus at the origin, then it can be changed into 1.8 with g x x2n−1 a2n−1 O x , n ≥ 2, a2n−1 > 0. 1.9 According to 11 under 1.9 by a change of variables x a...

We investigate responses of a model for intracellular Ca2+ oscillations to external pulsatile forcing in the presence of additive Gaussian noise. Our results show that noise makes the system less susceptible to external forcing and thus enhances robustness of Ca2+ oscillations. The results can be well explained by the local divergence of limit cycles in the phase space.  2003 Elsevier B.V. All...