Abstract: A mathematical model for knowledge acquisition in
teaching and learning is proposed. In this study we adopt the
mathematical model that is normally used for disease modelling
into teaching and learning. We derive mathematical conditions which
facilitate knowledge acquisition. This study compares the effects
of dropping out of the course at early stages with later stages of
learning. The study also investigates effect of individual interaction
and learning from other sources to facilitate learning. The study fits
actual data to a general mathematical model using Matlab ODE45
and lsqnonlin to obtain a unique mathematical model that can be
used to predict knowledge acquisition. The data used in this study
was obtained from the tutorial test results for mathematics 2 students
from the Central University of Technology, Free State, South Africa
in the department of Mathematical and Physical Sciences. The study
confirms already known results that increasing dropout rates and
forgetting taught concepts reduce the population of knowledgeable
students. Increasing teaching contacts and access to other learning
materials facilitate knowledge acquisition. The effect of increasing
dropout rates is more enhanced in the later stages of learning
than earlier stages. The study opens up a new direction in further
investigations in teaching and learning using differential equations.
Abstract: Crop yield prediction is a paramount issue in
agriculture. The main idea of this paper is to find out efficient
way to predict the yield of corn based meteorological records.
The prediction models used in this paper can be classified into
model-driven approaches and data-driven approaches, according to
the different modeling methodologies. The model-driven approaches are based on crop mechanistic
modeling. They describe crop growth in interaction with their
environment as dynamical systems. But the calibration process of
the dynamic system comes up with much difficulty, because it
turns out to be a multidimensional non-convex optimization problem.
An original contribution of this paper is to propose a statistical
methodology, Multi-Scenarios Parameters Estimation (MSPE), for the
parametrization of potentially complex mechanistic models from a
new type of datasets (climatic data, final yield in many situations).
It is tested with CORNFLO, a crop model for maize growth. On the other hand, the data-driven approach for yield prediction
is free of the complex biophysical process. But it has some strict
requirements about the dataset.
A second contribution of the paper is the comparison of these
model-driven methods with classical data-driven methods. For this
purpose, we consider two classes of regression methods, methods
derived from linear regression (Ridge and Lasso Regression, Principal
Components Regression or Partial Least Squares Regression) and
machine learning methods (Random Forest, k-Nearest Neighbor,
Artificial Neural Network and SVM regression).
The dataset consists of 720 records of corn yield at county scale
provided by the United States Department of Agriculture (USDA) and
the associated climatic data. A 5-folds cross-validation process and
two accuracy metrics: root mean square error of prediction(RMSEP),
mean absolute error of prediction(MAEP) were used to evaluate the
crop prediction capacity.
The results show that among the data-driven approaches, Random
Forest is the most robust and generally achieves the best prediction
error (MAEP 4.27%). It also outperforms our model-driven approach
(MAEP 6.11%). However, the method to calibrate the mechanistic
model from dataset easy to access offers several side-perspectives.
The mechanistic model can potentially help to underline the stresses
suffered by the crop or to identify the biological parameters of interest
for breeding purposes. For this reason, an interesting perspective is
to combine these two types of approaches.
Abstract: This paper considers an H∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H∞ TS fuzzy state-derivative feedback control law which guarantees L2-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.
Abstract: In this paper, we considered and applied parametric
modeling for some experimental data of dynamical system. In this
study, we investigated the different distribution of output
measurement from some dynamical systems. Also, with variance
processing in experimental data we obtained the region of
nonlinearity in experimental data and then identification of output
section is applied in different situation and data distribution. Finally,
the effect of the spanning the measurement such as variance to
identification and limitation of this approach is explained.
Abstract: We present a hybrid architecture of recurrent neural
networks (RNNs) inspired by hidden Markov models (HMMs). We
train the hybrid architecture using genetic algorithms to learn and
represent dynamical systems. We train the hybrid architecture on a
set of deterministic finite-state automata strings and observe the
generalization performance of the hybrid architecture when presented
with a new set of strings which were not present in the training data
set. In this way, we show that the hybrid system of HMM and RNN
can learn and represent deterministic finite-state automata. We ran
experiments with different sets of population sizes in the genetic
algorithm; we also ran experiments to find out which weight
initializations were best for training the hybrid architecture. The
results show that the hybrid architecture of recurrent neural networks
inspired by hidden Markov models can train and represent dynamical
systems. The best training and generalization performance is
achieved when the hybrid architecture is initialized with random real
weight values of range -15 to 15.
Abstract: This paper presents anti-synchronization of chaos
between two different chaotic systems using active control method.
The proposed technique is applied to achieve chaos antisynchronization
for the Lü and Rössler dynamical systems.
Numerical simulations are implemented to verify the results.
Abstract: In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.
Abstract: This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.