Exploring the effects of prescribed fire on ticks spread and propagation in a spatial setting

Lyme disease is one of the most prominent tick-borne diseases in the United States and prevalence of the disease has been steadily increasing over the past several decades due to a number of factors, including climate change. Methods for control of the disease have been considered, one of which is prescribed burning. In this paper the effects of prescribed burns on the abundance of ticks present in a spatial domain are assessed. A spatial stage-structured tick-host model with an impulsive differential equation system is developed to simulate the effect that controlled burning has on tick populations. Subsequently, a global sensitivity analysis is performed to evaluate the effect of various model parameters on the prevalence of infectious nymphs. Results indicate that while ticks can recover relatively quickly following a burn, yearly, high-intensity prescribed burns can reduce the prevalence of ticks in and around the area that is burned. The use of prescribed burns in preventing the establishment of ticks into new areas is also explored and it is observed that frequent burning can slow establishment considerably.

The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

The Parametric Optimization of Voltage Multiplier

The evolutionary model of voltage multiplier parametric optimization which includes 5 diodes and 5 capacitors is reviewed. It executes the transformation of alternating into constant voltage using a five times larger amplitude. The valve work is modelled according to the scheme of an ideal key. The original mathematical model of voltage multiplier which includes additional logical variables is deducted. It aссepts binary meanings 0 and 1, where 0 corresponds to closed valve status and 1 corresponds to open. In order to receive such a model, it is necessary to indicate the amount of open and closed valve combinations. Then for each of them, it is necessary to write the system of differential equations. Comparing them with each other the single differential equation system with additional logical variables is written as a generalization. The evolutional model is used in order to select the capacitor volume meaning. The goal function forecasts two conditions: maximum meaning of output voltage 1 kV and its minimal fluctuations in the stable regime.

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

Implementation of the variation of the luni-solar acceleration into GLONASS orbit calculus

In the differential equation system describes the motion of GLONASS satellites (rus. Globalnaya Navigazionnaya Sputnikovaya Sistema, or Global Navigation Satellite System ), the acceleration caused by the luni-solar traction is often taken as a constant during the period of the integration. In this work-study, we assume that the acceleration due to the luni-solar traction is not constant but varies linearly during the period of integration following this assumption; the linear functions in the three axes of the luni-solar acceleration are computed for an interval of 30 min and then implemented into the differential equations. The use of the numerical integration of Runge-Kutta fourth-order is recommended in the GLONASS-ICD (Interface Control Document) to solve for the differential equation system in order to get an orbit solution. The computation of the position and velocity of a GLONASS satellite in this study is performed by using the Runge-Kutta fourth-order method in forward and backward integration, with initial conditions provided in the broadcast ephemerides file.

Stability of Non-Hyperbolic Equilibrium Point for Polynomial System of Differential Equations

In this paper, a polynomial system of plane differential equations is observed. The stability of the non-hyperbolic equilibrium point was analyzed using normal forms. The nonlinear part of the differential equation system is simplified to the maximum. Two nonlinear transformations were used to simplify first the quadratic and then the cubic part of the system of equations.

Data Analysis of Physical Fitness Monitoring Based on Mathematical Models

Physical monitoring and analysis are of great significance to improve national physical fitness. The main work of this paper is that the physical health level of college students is studied and analysed by using a statistical model and mathematical model. According to the characteristics of the collected data, different mathematical models are established. Firstly, the grey correlation model is used to analyse the correlation between pull-up and other physical fitness indexes. Then, based on the classification of college students and the influence and flow law of interclass crowd, a differential equation system is established based on the LMC model. By analysing the existence and stability of the equilibrium point of the system, as well as the possible folding bifurcation and backward bifurcation at the equilibrium point, this paper makes qualitative and quantitative research on the trend of college students’ physical exercise on campus.

New variational theory for coupled nonlinear fractal Schrödinger system

Purpose The purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems. Design/methodology/approach The coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory. Findings The fractal variational iteration transform method is an excellent method to solve the fractal differential equation system. Originality/value The author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.

The Second-Order Differential Equation System with the Controlled Process for Variational Inequality with Constraints

In this paper, the variational inequality with constraints can be viewed as an optimization problem. Using Lagrange function and projection operator, the equivalent operator equations for the variational inequality with constraints under the certain conditions are obtained. Then, the second-order differential equation system with the controlled process is established for solving the variational inequality with constraints. We prove that any accumulation point of the trajectory of the second-order differential equation system is a solution to the variational inequality with constraints. In the end, one example with three kinds of different cases by using this differential equation system is solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the controlled process for solving the variational inequality with constraints.