Abstract: Today, the treatment of cancer, in a relatively short
period, with minimum adverse effects is a great concern for
oncologists. In this paper, based on a recently used mathematical
model for cancer, a guideline has been proposed for the amount
and duration of drug doses for cancer treatment by immunotherapy.
Dynamically speaking, the mathematical ordinary differential
equation (ODE) model of cancer has different equilibrium points;
one of them is unstable, which is called the no tumor equilibrium
point. In this paper, based on the number of tumor cells an
intelligent soft computing controller (a combination of fuzzy logic
controller and genetic algorithm), decides regarding the amount
and duration of drug doses, to eliminate the tumor cells and
stabilize the unstable point in a relatively short time. Two different
immunotherapy approaches; active and adoptive, have been studied
and presented. It is shown that the rate of decay of tumor cells is
faster and the doses of drug are lower in comparison with the result
of some other literatures. It is also shown that the period of
treatment and the doses of drug in adoptive immunotherapy are
significantly less than the active method. A recommendation to
oncologists has also been presented.
Abstract: This paper investigated the simulation of two-phase interleaved boost converter (IBC) with free and open-source software Scilab/Xcos. By using interleaved method, it can reduce current stress on components, components size, input current ripple and output voltage ripple. The required mathematical model is obtained from the equivalent circuit of its different four modes of operation for simulation. The equivalent circuits are considered in continuous conduction mode (CCM). The average values of the system variables are derived from the state-space equation to find the equilibrium point. Scilab is now becoming more and more popular among students, engineers and scientists because it is open-source software and free of charge. It gives a great convenience because it has powerful computation and simulation function. The waveforms of output voltage, input current and inductors current are obtained by using Scilab/Xcos.
Abstract: In this paper, we analyse the stability of the SEIR model
of malaria with infective immigrants which was recently formulated
by the authors. The model consists of an SEIR model for the human
population and SI Model for the mosquitoes. Susceptible humans
become infected after they are bitten by infectious mosquitoes and
move on to the Exposed, Infected and Recovered classes respectively.
The susceptible mosquito becomes infected after biting an infected
person and remains infected till death. We calculate the reproduction
number R0 using the next generation method and then discuss about
the stability of the equilibrium points. We use the Lyapunov function
to show the global stability of the equilibrium points.
Abstract: For the synchronous generator simulation and analysis and for the power system stabilizer design and synthesis a mathematical model of synchronous generator is needed. The model has to accurately describe dynamics of oscillations, while at the same time has to be transparent enough for an analysis and sufficiently simplified for design of control system. To study the oscillations of the synchronous generator against to the rest of the power system, the model of the synchronous machine connected to an infinite bus through a transmission line having resistance and inductance is needed. In this paper, the linearized reduced order dynamic model of the synchronous generator connected to the infinite bus is presented and analysed in details. This model accurately describes dynamics of the synchronous generator only in a small vicinity of an equilibrium state. With the digression from the selected equilibrium point the accuracy of this model is decreasing considerably. In this paper, the equations’ descriptions and the parameters’ determinations for the linearized reduced order mathematical model of the synchronous generator are explained and summarized and represent the useful origin for works in the areas of synchronous generators’ dynamic behaviour analysis and synchronous generator’s control systems design and synthesis. The main contribution of this paper represents the detailed analysis of the accuracy of the linearized reduced order dynamic model in the entire synchronous generator’s operating range. Borders of the areas where the linearized reduced order mathematical model represents accurate description of the synchronous generator’s dynamics are determined with the systemic numerical analysis. The thorough eigenvalue analysis of the linearized models in the entire operating range is performed. In the paper, the parameters of the linearized reduced order dynamic model of the laboratory salient poles synchronous generator were determined and used for the analysis. The theoretical conclusions were confirmed with the agreement of experimental and simulation results.
Abstract: This work explores the inter-region investment
behaviors of Integrated Circuit (IC) design industry from Taiwan to
China using the amount of foreign direct investment (FDI). According
to the mutual dependence among different IC design industrial
locations, Lotka-Volterra model is utilized to explore the FDI
interactions between South and East China. Effects of inter-regional
collaborations on FDI flows into China are considered. The analysis
results show that FDIs into South China for IC design industry
significantly inspire the subsequent FDIs into East China, while FDIs
into East China for Taiwan’s IC design industry significantly hinder
the subsequent FDIs into South China. Because the supply chain along
IC industry includes upstream IC design, midstream manufacturing, as
well as downstream packing and testing enterprises, IC design industry
has to cooperate with IC manufacturing, packaging and testing
industries in the same area to form a strong IC industrial cluster.
Taiwan’s IC design industry implement the largest FDI amount into
East China and the second largest FDI amount into South China
among the four regions: North, East, Mid-West and South China. If IC
design houses undertake more FDIs in South China, those in East
China are urged to incrementally implement more FDIs into East
China to maintain the competitive advantages of the IC supply chain in
East China. On the other hand, as the FDIs in East China rise, the FDIs
in South China will successively decline since capitals have
concentrated in East China. In addition, this investigation proves that
the prediction of Lotka-Volterra model in FDI trends is accurate
because the industrial interactions between the two regions are
included. Finally, this work confirms that the FDI flows cannot reach a
stable equilibrium point, so the FDI inflows into East and South China
will expand in the future.
Abstract: This paper discusses the performance of critical
trajectory method (CTrj) for power system transient stability analysis
under various loading settings and heavy fault condition. The method
obtains Controlling Unstable Equilibrium Point (CUEP) which is
essential for estimation of power system stability margins. The CUEP
is computed by applying the CTrjto the boundary controlling unstable
equilibrium point (BCU) method. The Proposed method computes a
trajectory on the stability boundary that starts from the exit point and
reaches CUEP under certain assumptions. The robustness and
effectiveness of the method are demonstrated via six power system
models and five loading conditions. As benchmark is used
conventional simulation method whereas the performance is compared
with and BCU Shadowing method.
Abstract: Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.
Abstract: In the following article we begin from a multi-parameter unstable nonlinear model of a Quadrotor. We design a control to stabilize and assure the attitude of the device, starting off a linearized system at the equilibrium point of the null angles of Euler (hover),
which provides us a control with limited capacities at small angles of rotation of the vehicle in three dimensions. In order to clear this obstacle, we propose the identification of models in different angles by means of simulations and the design of a controller specifically implemented for the identification task, that in future works will allow the development of controllers according to fast and agile angles of Euler for Quadrotor.
Abstract: In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.
Abstract: This paper studies the effect of time delay on stability
of mutualism population model with limited resources for both
species. First, the stability of the model without time delay is
analyzed. The model is then improved by considering a time delay in
the mechanism of the growth rate of the population. We analyze the
effect of time delay on the stability of the stable equilibrium point.
Result showed that the time delay can induce instability of the stable
equilibrium point, bifurcation and stability switches.
Abstract: In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.
Abstract: This paper proposes a solution to the motion planning
and control problem of a point-mass robot which is required to move
safely to a designated target in a priori known workspace cluttered
with fixed elliptical obstacles of arbitrary position and sizes. A
tailored and unique algorithm for target convergence and obstacle
avoidance is proposed that will work for any number of fixed
obstacles. The control laws proposed in this paper also ensures that
the equilibrium point of the given system is asymptotically stable.
Computer simulations with the proposed technique and applications
to a planar (RP) manipulator will be presented.
Abstract: In this paper, a class of impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms is formulated and investigated. By employing the delay differential inequality and inequality technique developed by Xu et al., some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.
Abstract: The next generation wireless systems, especially the
cognitive radio networks aim at utilizing network resources more
efficiently. They share a wide range of available spectrum in an
opportunistic manner. In this paper, we propose a quality
management model for short-term sub-lease of unutilized spectrum
bands to different service providers. We built our model on
competitive secondary market architecture. To establish the
necessary conditions for convergent behavior, we utilize techniques
from game theory. Our proposed model is based on potential game
approach that is suitable for systems with dynamic decision making.
The Nash equilibrium point tells the spectrum holders the ideal price
values where profit is maximized at the highest level of customer
satisfaction. Our numerical results show that the price decisions of
the network providers depend on the price and QoS of their own
bands as well as the prices and QoS levels of their opponents- bands.
Abstract: Mathematical models can be used to describe the
dynamics of the spread of infectious disease between susceptibles
and infectious populations. Dengue fever is a re-emerging disease in
the tropical and subtropical regions of the world. Its incidence has
increased fourfold since 1970 and outbreaks are now reported quite
frequently from many parts of the world. In dengue endemic regions,
more cases of dengue infection in pregnancy and infancy are being
found due to the increasing incidence. It has been reported that
dengue infection was vertically transmitted to the infants. Primary
dengue infection is associated with mild to high fever, headache,
muscle pain and skin rash. Immune response includes IgM antibodies
produced by the 5th day of symptoms and persist for 30-60 days. IgG
antibodies appear on the 14th day and persist for life. Secondary
infections often result in high fever and in many cases with
hemorrhagic events and circulatory failure. In the present paper, a
mathematical model is proposed to simulate the succession of dengue
disease transmission in pregnancy and infancy. Stability analysis of
the equilibrium points is carried out and a simulation is given for the
different sets of parameter. Moreover, the bifurcation diagrams of our
model are discussed. The controlling of this disease in infant cases is
introduced in the term of the threshold condition.
Abstract: In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.
Abstract: The dynamics of a predator-prey model with continuous
threshold policy harvesting functions on the prey is studied. Theoretical
and numerical methods are used to investigate boundedness
of solutions, existence of bionomic equilibria, and the stability properties
of coexistence equilibrium points and periodic orbits. Several
bifurcations as well as some heteroclinic orbits are computed.
Abstract: In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.
Abstract: In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.
Abstract: In this paper we study a food chain model with three trophic levels and Michaelis-Menten type ratio-dependent functional response. Distinctive feature of this model is the sensitive dependence of the dynamical behavior on the initial populations and parameters of the real world. The stability of the equilibrium points are also investigated.