Search results for "nonlinear problem"
showing 4 items of 4 documents
Periodic and Chaotic Orbits of a Neuron Model
2015
In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.
Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems
2019
[EN] Searching zeros of nonlinear functions often employs iterative procedures. In this paper, we construct several families of iterative methods with memory from one without memory, that is, we have increased the order of convergence without adding new functional evaluations. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Moreover, we have found some elements of the family whose behavior includes strange attractors of different kinds that must be avoided in practice. In this sense, Feigenbaum diagrams have resulted an extremely …
Periodic orbits of single neuron models with internal decay rate 0 < β ≤ 1
2013
In this paper we consider a discrete dynamical system x n+1=βx n – g(x n ), n=0,1,..., arising as a discrete-time network of a single neuron, where 0 < β ≤ 1 is an internal decay rate, g is a signal function. A great deal of work has been done when the signal function is a sigmoid function. However, a signal function of McCulloch-Pitts nonlinearity described with a piecewise constant function is also useful in the modelling of neural networks. We investigate a more complicated step signal function (function that is similar to the sigmoid function) and we will prove some results about the periodicity of solutions of the considered difference equation. These results show the complexity of …
A posteriori error identities for nonlinear variational problems
2015
A posteriori error estimation methods are usually developed in the context of upper and lower bounds of errors. In this paper, we are concerned with a posteriori analysis in terms of identities, i.e., we deduce error relations, which holds as equalities. We discuss a general form of error identities for a wide class of convex variational problems. The left hand sides of these identities can be considered as certain measures of errors (expressed in terms of primal/dual solutions and respective approximations) while the right hand sides contain only known approximations. Finally, we consider several examples and show that in some simple cases these identities lead to generalized forms of the …