Liénard systems of the form ẍ + ǫf(x)ẋ + x = 0, with f(x) an even continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak (ǫ → 0) and in the strongly (ǫ → ∞) nonlinear regime in some examples. The number of limit cycles does not increase when ǫ increases from zero to infinity in all the cases analyzed.

One way to formulate the Hilbert 16-th Problem is the following: Hilbert 16-th Problem (HP). Find an estimate for H(n) for any n ∈ Z+. We shall discuss problems related to the following: Existential Hilbert 16-th Problem (EHP). Prove that H(n) < ∞ for any n ∈ Z+. The problem about finiteness of number of limit cycles for an individual polynomial line field (1) is called Dulac problem since the ...

Rate and magnitude control limitations are often responsible for the apparition of undesired limit-cycles in the resulting nonlinear closed-loop system. Based on the wellknown describing function approach, it is shown in this paper that such limit cycles can be avoided as soon as H∞ constraints are simultaneously satisfied by appropriately chosen linear interconnections. This result is then use...

In this paper we study the maximum number of limit cycles of the following generalized Liénard polynomial differential system of the first order ẋ = y2p−1 ẏ = −x2q−1 − εf (x, y) where p and q are positive integers, ε is a small parameter and f (x, y) is a polynomial of degree m. We prove that this maximum number depends on p, q and m. AMS subject classification:

We prove that the property to be limit aperiodic is preserved by the standard construction with groups like extension, HNN extension and free product. We also construct a non-limit aperiodic G-space.

Pattern formation via synchronization and oscillator death is considered in networks of diffusively coupled limit-cycle oscillators. Different examples of patterns and their dynamics are presented including nontrivial effects such as: (i) synchronized clusters induced by disorder and (ii) transitions from non-propagation to propagation of fronts via the intermittency. © 2002 IMACS. Published by...

We show that the problem of computing the vacuum expectation values of gauge invariant operators in the strong coupling limit of topologically massive gauge theory is equivalent to the problem of computing similar operators in the G k /G model where k is the integer coefficient of the Chern-Simons term. The G k /G model is a topological field theory and many correlators can be computed analytic...

This paper presents results for the aeroelastic stability and LCO behavior for a complete aircraft. Comparison are presented between the results predicted by a cantilevered wing model, an untrimmed aircraft model (no gravity or drag) and a trimmed aircraft model. It is seen that the stability behavior is predicted accurately only if the correct trim loads are applied to the wing. The LCO behavi...

This paper deals mainly with generalizations of results in nitary combinatorics to innnite ordinals. It is well-known that for nite ordinals P << is the number of 2-element subsets of an-element set. It is shown here that for any well-ordered set of arbitrary innnite order type , P << is the ordinal of the set M of 2-element subsets where M is ordered in some natural way. This result is then ex...

In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved.