Mathematics and Computers in Simulation最新文献

Identification of the various dynamical kinetics relating to prey–predator interconnection is the main goal of theoretical ecologists. In addition to direct killing (the lethal effect) in prey–predator interactions, a number of studies have suggested that there are some indirect effects (non-lethal), such as fear of predation. This non-lethal effect slows down the growth rate of prey and this phenomenon can be carried over to upcoming seasons or generations. The Allee effect also has an impact not only on prey populations but also on predator populations. Considering these, we first propose a modified Leslie–Gower predator–prey model that takes into account the fear-induced carry-over effect (COE), the predator’s Allee effect, and intraspecific competition among predators. The ecologically viable equilibrium points and corresponding local and global stability criteria are derived for the model. Moreover, we establish the conditions for the occurrence of Hopf-bifurcation around coexistence equilibrium and compute the first Lyapunov coefficient to verify the stability of the limit cycle. Secondly, we extend the proposed model to include the spatial variable by considering the spatial movements of the species. For the spatial model with zero flux boundary conditions, the criteria for Turing instability and Hopf-bifurcation are derived. Numerical simulations aim to verify the theoretical results. Our study suggests that the parameters related to fear-induced COE, the predator’s Allee effect, and intraspecific competition have a greater impact on system dynamics.

The paper presents a class of predator–prey model with density-dependent diffusion in the spatially heterogeneous environment. We first provide the global existence and boundedness of the solution for the model. Then, by taking a variable transformation, the difficulty brought by the cross-diffusion can be overcome, and the existence, stability and local bifurcation of semi-trivial steady-state solutions for the equivalent system are further studied. Finally, the existence of positive solutions of the system is also given by using the Leray–Schauder degree theory and the method of principle eigenvalue, especially for the limit cases when the diffusion coefficient tends to zero or infinite.

A perpetual American strangle option refers to an investment strategy combining the features of both call and put options on a single underlying asset, with an infinite time horizon. Investors are known to use this trading strategy when they expect the stock price to fluctuate significantly but cannot predict whether it will rise or fall. In this study, we consider the perpetual American strangle options under a stochastic volatility model and investigate the corrected option values and free boundaries using an asymptotic analysis technique. Further, we examine the pricing accuracy of the approximated formulas for perpetual American strangle options under stochastic volatility by comparing our solutions with the prices that are obtained from Monte Carlo simulations. We also investigate the sensitivities of the option values and free boundaries with respect to several model parameters.

In this paper, we first formulate an average finite difference scheme with appropriate correction terms for the time-fractional initial-value problem of $y^{\prime }\left(t\right){+}_0^{RL}{D}_t^{1-\alpha }y\left(t\right)=g\left(t\right)$, where ${}_0^{RL}{D}_t^{1-\alpha }$ denotes the Riemann–Liouville fractional derivative of order $1-\alpha$ $(\alpha \in (0,1))$. It is shown that, under some suitable conditions on the data, the numerical solution converges to the exact solution with order $O\left({\tau }^2\right)$, where $\tau$ is the time step size. The method is then extended to solve the time-fractional Cable equation, combined with a standard discretisation of the spatial derivatives on a uniform mesh. The second-order time convergence rate is proved. Several numerical examples are given to illustrate the good agreement with the theoretical analysis of the presented methods.

This study proposes a novel tool for neural network modeling by integrating quaternion theory, discrete fractional calculus, and stochastic analysis, thereby introducing a stochastic discrete fractional delayed quaternion-valued neural network model. Firstly, we prove the existence and uniqueness of the equilibrium point for the model by using the homeomorphism mapping theory. Secondly, we give some new inequalities in the quaternion domain. Through these inequalities and Lyapunov theory, we establish sufficient linear matrix inequality (LMI) conditions on the global mean square stability and global mean square Mittag-Leffler stability for the model. Furthermore, the linear feedback control approach is employed to derive sufficient LMI conditions that achieve the model’s global mean square synchronization and global mean square Mittag-Leffler synchronization. Finally, several numerical examples validate the findings obtained.

In this article, we address the solution of advection-dominated flow problems by stabilized methods, by means of data-driven least-squares computed stabilized coefficients. As main methodological tool, we introduce a data-driven off-line/on-line strategy to compute them with low computational cost.

We compare the errors provided by the data-driven stabilized coefficients to those provided by several previously established stabilized coefficients within the solution of advection–diffusion and Navier–Stokes flows, on structured and un-structured grids, with Lagrange Finite Elements up to third degree of interpolation. We obtain substantial error improvements for high-order finite element interpolation.

We conclude that the data-driven procedure is a rewarding procedure, worth to be applied to general stabilized solutions of general flow problems.

In this paper, we propose a mathematical model using the Caputo fractional derivative (CFD) and two control signals to study the transmission dynamics and control of Chickenpox (Varicella) outbreak. The model consists of six compartments representing susceptible, vaccinated, exposed, infected with complications, infected without complications, and recovered individuals. We analyze the theoretical properties of the model, including existence, uniqueness, and boundedness of solutions, and calculate the basic reproduction number $\left(R_0\right)$. We identify equilibrium points and establish conditions for their stability. Sensitivity analysis helps identify the most influential parameters on $R_0$. We formulate a fractional optimal control problem (FOCP) by incorporating time-dependent prevention and isolation measures. The necessary optimality conditions are derived using Pontryagin’s maximum principle. Numerical simulations based on the Adams–Bashforth–Moulton (ABM) method illustrate the impact of control measures and fractional order on disease propagation. The results highlight the effectiveness of optimal controls and fractional order in understanding and managing epidemics, enhancing stability conditions. The study contributes to a better understanding of Chickenpox transmission dynamics and provides insights for disease control and management, aiding decision-makers and governments in taking preventive measures.

This paper deals with the problem of sampled-data-based $H_{\infty }$ control design for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) subject to actuator failures. First, the Takagi-Sugeno (T-S) fuzzy system is employed to handle the nonlinearities of presented model. Next, by employing a Bernoulli stochastic variable, the general scenario of switched coupling memory sampled-data control (CMSDC) is designed which contains the sampled-data control (SDC) and memory SDC scheme as special cases. By combining the membership function-dependent (MFD) asymmetric looped-type Lyapunov-Krasovskii functional (LKF) and employing the available information of membership functions in $H_{\infty }$ performance, the delay-dependent stabilization conditions of considered PMSG-based WTS are derived through the switched CMSDC technique. Meanwhile, the disturbances of considered systems are attenuated by taking the advantage of the newly proposed MFD $H_{\infty }$ performance. Eventually, the simulation results are given to demonstrate the efficacy and applicability of the proposed CMSDC technique.