In this note we consider a collection C of one parameter families of unimodal maps of [0, 1]. Each family in the collection has the form {μf} where μ ∈ [0, 1]. Denoting the kneading sequence of μf by K(μf), we will prove that for each member of C, the map μ 7→ K(μf) is monotone. For interest, μf(x) = 4μx(1− x) and μf(x) = μ sin(πx) are shown to belong to C. This extends the work of Masato Tsuji...

Let W be a weight–homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this result to a particular family of planar polynomial systems having a nilpotent center without meromorphic first integral. 2000 AMS Subject Classification: 34C07, ...

We consider a FitzHugh-Nagumo Reaction-Diffusion type system (FHN). The dynamics of the reaction part induces a unique repulsive stationnary point (0, 0) and a unique attractive limit cycle. After a description of the asymptotic behaviour of the FHN system, we deal with the synchronization and control analysis of N coupled FHN systems.

This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples ...

In this paper, a quadratic system with two parallel straight line-isoclines is considered. This system corresponds to the system of class II in the classification of Ye Yanqian [13]. Using the field rotation parameters of the constructed canonical system and geometric properties of the spirals filling the interior and exterior domains of its limit cycles, we prove that the maximum number of lim...

Valve nonlinearities are responsible for producing limit cycles in the loop and consequently decreasing plant performance. In the case of an integrating plant, once the loop oscillation is detected, the engineer should distinguish between stiction and backlash, but no method is available in the literature to address this class of problem. In this paper, it is proposed a data-driven method to di...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We consider number of limit cycles of perturbed quintic Hamiltonian system with perturbation in the form of (2n+2m) or (2n+2m+1) degree polynomials. We show that the perturbed system has at most n + 2m limit cycles. For m = 1 and n = 1 we showed that the perturbed system can have at most one limit cycles. If m = 1 and n = 2 we give some general conditions based on coefficients of the perturbed ...

We provide lower bounds for the maximum number of limit cycles for the m–piecewise discontinuous polynomial differential equations ẋ = y + sgn(gm(x, y))F (x), ẏ = −x, where the zero set of the function sgn(gm(x, y)) with m = 2, 4, 6, . . . is the product of m/2 straight lines passing through the origin of coordinates dividing the plane in sectors of angle 2π/m, and sgn(z) denotes the sign funct...

In this paper we find an upper bound for the maximum number of limit cycles bifurcating from the periodic orbits of any planar polynomial quasi-homogeneous center, which can be obtained using first order averaging method. This result improves the upper bounds given in [7].