scholarly journals About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Eloy Irigoyen ◽  
Antonio Javier Barragán ◽  
Mikel Larrea ◽  
José Manuel Andújar
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Nonlinear Systems ◽  
Dynamic Behaviour ◽  
Equilibrium Points ◽  
Multilayer Perceptrons ◽  
State Variables ◽  
Dynamic Information ◽  
Universal Approximators ◽  
Operating Points

This work presents a straightforward methodology based on neural networks (NN) which allows to obtain relevant dynamic information of unknown nonlinear systems. It provides an approach for cases in which the complex task of analyzing the dynamic behaviour of nonlinear systems makes it excessively challenging to obtain an accurate mathematical model. After reviewing the suitability of multilayer perceptrons (MLPs) as universal approximators to replace a mathematical model, the first part of this work presents a system representation using a model formulated with state variables which can be exported to a NN structure. Considering the linearization of the NN model in a mesh of operating points, the second part of this work presents the study of equilibrium states in such points by calculating the Jacobian matrix of the system through the NN model. The results analyzed in three case studies provide representative examples of the strengths of the proposed method. Conclusively, it is feasible to study the system behaviour based on MLPs, which enables the analysis of the local stability of the equilibrium points, as well as the system dynamics in its environment, therefore obtaining valuable information of the system dynamic behaviour.

scholarly journals Optimizing the Kaplan–Yorke Dimension of Chaotic Oscillators Applying DE and PSO

Technologies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 38 ◽  
Author(s):  
Alejandro Silva-Juarez ◽  
Gustavo Rodriguez-Gomez ◽  
Luis Gerardo de la Fraga ◽  
Omar Guillen-Fernandez ◽  
Esteban Tlelo-Cuautle
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
Color Image ◽  
Equilibrium Points ◽  
Computing Time ◽  
Chaotic Oscillator ◽  
State Variables ◽  
Huge Number ◽  
Chaotic Oscillators ◽  
Swarm Optimization

When a new chaotic oscillator is introduced, it must accomplish characteristics like guaranteeing the existence of a positive Lyapunov exponent and a high Kaplan–Yorke dimension. In some cases, the coefficients of a mathematical model can be varied to increase the values of those characteristics but it is not a trivial task because a very huge number of combinations arise and the required computing time can be unreachable. In this manner, we introduced the optimization of the Kaplan–Yorke dimension of chaotic oscillators by applying metaheuristics, e.g., differential evolution (DE) and particle swarm optimization (PSO) algorithms. We showed the equilibrium points and eigenvalues of three chaotic oscillators that are simulated applying ODE45, and the Kaplan–Yorke dimension was evaluated by Wolf’s method. The chaotic time series of the state variables associated to the highest Kaplan–Yorke dimension provided by DE and PSO are used to encrypt a color image to demonstrate that they are useful in implementing a secure chaotic communication system. Finally, the very low correlation between the chaotic channel and the original color image confirmed the usefulness of optimizing Kaplan–Yorke dimension for cryptographic applications.

scholarly journals The Use of Artificial Neural Networks and a General Discriminant Analysis for Predicting Culling Reasons in Holstein-Friesian Cows Based on First-Lactation Performance Records

Animals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 721
Author(s):  
Krzysztof Adamczyk ◽  
Wilhelm Grzesiak ◽  
Daniel Zaborski
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Discriminant Analysis ◽  
Multilayer Perceptrons ◽  
Correct Classification ◽  
Correct Classification Rate ◽  
Classification Rate ◽  
Holstein Friesian ◽  
Artificial Neural ◽  
Friesian Cows

The aim of the present study was to verify whether artificial neural networks (ANN) may be an effective tool for predicting the culling reasons in cows based on routinely collected first-lactation records. Data on Holstein-Friesian cows culled in Poland between 2017 and 2018 were used in the present study. A general discriminant analysis (GDA) was applied as a reference method for ANN. Considering all predictive performance measures, ANN were the most effective in predicting the culling of cows due to old age (99.76–99.88% of correctly classified cases). In addition, a very high correct classification rate (99.24–99.98%) was obtained for culling the animals due to reproductive problems. It is significant because infertility is one of the conditions that are the most difficult to eliminate in dairy herds. The correct classification rate for individual culling reasons obtained with GDA (0.00–97.63%) was, in general, lower than that for multilayer perceptrons (MLP). The obtained results indicated that, in order to effectively predict the previously mentioned culling reasons, the following first-lactation parameters should be used: calving age, calving difficulty, and the characteristics of the lactation curve based on Wood’s model parameters.

scholarly journals Estimation of electrical resistivity using artificial neural networks: a case study from Lublin Basin, SE Poland

2021 ◽  
Author(s):  
Jakub Ważny ◽  
Michał Stefaniuk ◽  
Adam Cygal
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Training Data ◽  
Multilayer Perceptrons ◽  
Borehole Data ◽  
Geological Interpretation ◽  
Se Poland ◽  
Geological Conditions ◽  
Artificial Neural ◽  
Reliable Solution

AbstractArtificial neural networks method (ANNs) is a common estimation tool used for geophysical applications. Considering borehole data, when the need arises to supplement a missing well log interval or whole logging—ANNs provide a reliable solution. Supervised training of the network on a reliable set of borehole data values with further application of this network on unknown wells allows creation of synthetic values of missing geophysical parameters, e.g., resistivity. The main assumptions for boreholes are: representation of similar geological conditions and the use of similar techniques of well data collection. In the analyzed case, a set of Multilayer Perceptrons were trained on five separate chronostratigraphic intervals of borehole, considered as training data. The task was to predict missing deep laterolog (LLD) logging in a borehole representing the same sequence of layers within the Lublin Basin area. Correlation between well logs data exceeded 0.8. Subsequently, magnetotelluric parametric soundings were modeled and inverted on both boreholes. Analysis showed that congenial Occam 1D models had better fitting of TM mode of MT data in each case. Ipso facto, synthetic LLD log could be considered as a basis for geophysical and geological interpretation. ANNs provided solution for supplementing datasets based on this analytical approach.

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

Sign in / Sign up

Export Citation Format

Share Document