Analysis of a stochastic logistic model with diffusion

Stability analysis of a stochastic logistic model

Stability analysis of a stochastic logistic model with nonlinear diffusion term

The problem of target acquisition is considered to be a very involved process and is a serious challenge for the researchers. For several applications of target acquisition, it is worthwhile to compare the compressed and uncompressed images and the perceptual difference between the two images is also significant. A new neural network technique of image modeling by 2-D random fields formulated in the form of an autoregressive moving average process driven by input white Gaussian noise with known statistics is presented. The proposed technique consists of two stages: (1) estimating the parameters of the model and (2) regeneration of the image with the knowledge of the model, its parameters, initial conditions, and white noise. The problem of estimating the model parameters is formulated as an optimization problem solved by a single-layer neural network. Once the model parameters have been estimated as the adaptive weights of the network, the second stage reconstructs the picture from the model. This stage consists of recursively constructing the image using the initial conditions of the original image, the parameters of the model, and white Gaussian noise. Due to the adaptive nature and the computational capability of the neural network, a high-quality image is obtained with this approach. The proposed algorithm reduces the computational complexity and is recommended for the on-line image compression required in target-acquisition-type applications. As the image is constructed using fewer pixel values of the given image in the form of initial conditions, and a few parameters of the model, very effective image compression is achieved. Several computer simulation examples are included to illustrate the effectiveness of the proposed technique.

Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence, and global asymptotic stability are established. Moreover, the threshold between weak persistence and extinction is obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.

In this paper, we develop and study a stochastic logistic model by incorporating diffusion and two Ornstein–Uhlenbeck processes, which is a stochastic non-autonomous system. We first show the existence and uniqueness of the global solution of the system with any initial value. After that, we study the pth moment boundedness, asymptotic pathwise estimation, asymptotic behavior, and global attractivity of the solutions of the stochastic system in turn. Moreover, we establish sufficient criteria for the existence and uniqueness of a stationary distribution of positive solutions of the stochastic system with the help of Lyapunov function methods. It is worth mentioning that we derive the exact expression of the local probability density for the stochastic system by solving the relevant four-dimensional Fokker–Planck equation. We find that the smaller intensity of volatility or the bigger speed of reversion is helpful for preserving the biodiversity of the species. Finally, numerical simulations are performed to support our analytical findings.

Phenomenological bifurcation in a stochastic logistic model with correlated colored noises

A qualitative analysis of a cosmological model based on the asymmetric scalar doublet classical + phantom scalar field with minimal interaction is performed. It is shown that depending on the parameters of the model, the corresponding dynamical system can have 1, 3, or 9 stationary points corresponding to attractive or repulsive centers (1--5) and saddle points (0--4). A physical analysis of the model is performed.

In this paper, we analyze the dynamics of a new proposed stochastic non-autonomous SVIR model, with an emphasis on multiple stages of vaccination, due to the vaccine ineffectiveness. The parameters of the model are allowed to depend on time, to incorporate the seasonal variation. Furthermore, the vaccinated population is divided into three subpopulations, each one representing a different stage. For the proposed model, we prove the mathematical and biological well-posedness. That is, the existence of a unique global almost surely positive solution. Moreover, we establish conditions under which the disease vanishes or persists. Furthermore, based on stochastic stability theory and by constructing a suitable new Lyapunov function, we provide a condition under which the model admits a non-trivial periodic solution. The established theoretical results along with the performed numerical simulations exhibit the effect of the different stages of vaccination along with the stochastic Gaussian noise on the dynamics of the studied population.

Sensitivity analysis for models of population viability

Sensitivity analysis for models of population viability

The stochastic resonance system has the advantage of making the noise energy transfer to the signal energy. Because the existing stochastic resonance system model has the problem of poor performance, an asymmetric piecewise linear stochastic resonance system model is proposed, and the parameters of the model are optimized by a genetic algorithm. The signal-to-noise ratio formula of the model is derived and analyzed, and the theoretical basis for better performance of the model is given. The influence of the asymmetric coefficient on system performance is studied, which provides guidance for the selection of initial optimization range when a genetic algorithm is used. At the same time, the formula is verified and analyzed by numerical simulation, and the correctness of the formula is proved. Finally, the model is applied to bearing fault detection, and an adaptive genetic algorithm is used to optimize the parameters of the system. The results show that the model has an excellent detection effect, which proves that the model has great potential in fault detection.

Carrying Capacity and Demographic Stochasticity: Scaling Behavior of the Stochastic Logistic Model

IntroductionA model is an abstraction that reduces a problem to its essential characteristics. Mathematical models are useful because they exemplify the mathematical core of a situation without extraneous information. Models help to explain a system and to study the effects of different components, and to make predictions about behaviour. Analysis of model via computational and applied mathematical methods are ways to deduce the consequences of the interactions. It is the analysis of mathematical models that allows us to formalize the cause and effect process and tie it to the biological observations. Furthermore, model analysis yields insights into why a system behaves the way it does, thus providing links between network structure and behaviour.MethodologyStability natures of the critical points of the models at various values of the model parameters were investigated to determine the behaviour of the model solution. Eigenvalue sensitivity and Eigenvalue elasticity analyses were carried out to identify key parameters of the model which drive the solutions and to figure out the effect of proportional changes in parameter values on population growth of both diabetics with complications and diabetics with and without complications. Mathematical algorithms were coded in MATLAB computational environment to achieve these. The numerical solutions of the model at various values of the parameters were performed using Euler method and Runge-Kutta method of order four and compared with the analytic solution. The algorithms were coded with Maple software package.ResultThe stability analysis showed that the models were asymptotically stable at specified parameter values hence suitable for their intended purposes. The Eigenvalue sensitivity and Eigenvalue elasticity analyses showed the rate at which complications were controlled is the most important parameter of the model hence the policy lever for effective control of the size of diabetics with complications. The solutions were represented graphically at various values of prominent parameters.ConclusionThe population of diabetics will continue to increase for the time being, but the size of diabetics with complications can reduce drastically with comprehensive and concurrent treatment of Diabetes mellitus and its complications. Also with high rate of controlling complications of Diabetes mellitus and low probability of developing complications of the disease through interventions such as continuous education, reorientation, increase physical activities, balance nutrition, government and non-governmental support, the incidence of the disease reduce drastically.

Simulation-based sequential analysis of Markov switching stochastic volatility models

Profitability ratio maximization in an inventory model with stock-dependent demand rate and non-linear holding cost