Limit cycles of a perceptron

Limit cycles of a perceptron

An artificial neural network can be used to generate a series of numbers. A boolean perceptron generates bit sequences with a periodic structure. The corresponding spectrum of cycle lengths is investigated analytically and numerically; it has similarities with properties of rational numbers.

Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations

We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.

Limit Cycles of Differential

vol. 37 (2008) No. 1 Book review: LIMIT CYCLES OF DIFFERENTIAL EQUATIONS by Colin Christopher and Chengzhi Li In June 2006 Jaume Llibre and Armengol Gasull organized the Advan ed Course on Limit Cy les and Di erential Equations at the Centre de Re er a Matemàti a in Bar elona. There were three le turers: two by the authors of this book and by Sergey Yakovenko. The book under review ontains the ...

Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...

Perceptron beyond the limit of capacity