Nonlinear dynamics and chaos in a fractional-order HIV model.
New Q-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet conditions...
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.
This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to...
In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a...
Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for the second...
In the paper we present some guidelines for the application of nonparametric statistical tests and post-hoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that the pairwise Wilcoxon test, when employed to multiple comparisons, will lead to overoptimistic conclusions. We carry out intensive normality examination employing ten different tests showing that the...
Two decades ago, resistance distance was introduced to characterize “chemical distance” in (molecular) graphs. In this paper, we consider three resistance distance-based graph invariants, namely, the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index. Some Nordhaus-Gaddum-type results for these three molecular structure descriptors are obtained. In addition, a relation between these Kirchhoffian indices is established.
In this paper we study a linear population dynamics model. In this model, the birth process is described by a nonlocal term and the initial distribution is unknown. The aim of this paper is to use a controllability result of the adjoint system for the computation of the density of individuals at some time .
We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...