Global asymptotic stability of positive equilibrium in a 3-species cooperating model with time delay

The asymptotic behavior of the time-dependent solution for a 3-species cooperating model was investigated with the effects of both diffusion and time delay taken into consideration. We proved the global asymptotic stability of a positive steady-state solution to the model problem by using coupled upper and lower solutions for a more general reaction-diffusion system that gives a common framework for 3-species cooperating model problems. The result of global asymptotic stability implies that the model system coexistence is permanent. Some global asymptotic stability results for 2-species cooperating reaction-diffusion systems are included in the discussion, and some known results are extended.

Dynamic Modelling of a Hybrid Variable Reluctance Machine Using the 3D Finite Element Method

This paper presents the work carried out to evaluate the dynamic performance of the Hybrid Variable Reluctance Motor (HVRM). The fourth-order Runge-Kutta integration algorithm was employed to solve the equations of the dynamic model, in conjunction with the three-dimensional finite element method. The 3D numerical data was calculated using Comsol Multiphysics, which accounts for the nonlinearity of the ferromagnetic material and the 3D nature of the HVRM. The outcomes of this study are precise and accurately predict the dynamic behaviour of the HVRM in terms of rotor position response, rotational speed and torque. The distinctive contribution of this work lies in the 3D numerical modelling of the HVRM and the subsequent evaluation and analysis of its dynamic operation. Analytical and numerical 2D studies are less resource-intensive and time-consuming, and are more straightforward and rapid to analyse and interpret. However, they are constrained in their capacity to examine spatial, volumetric interactions and intricate dynamics such as flux studies where three 3D effects cannot be disregarded, winding end effects and the configuration and positioning of the interposed permanent magnet.

Equilibrium Positions of a Cable-Connected Satellites System under Several Influences

The present paper deals with the study of equilibrium positions of the motion of a system of two artificial satellites connected by a light, flexible, inextensible and non-conducting cable under the influence of solar radiation pressure, earth’s oblateness, shadow of the earth and air resistance. Here, we study the case of circular orbit of the centre of mass of the system. We derive differential equations of motion of the system. General solutions of the differential equations are beyond the reach. On the other hand, the general solutions do not serve our purpose. Jacobian integral of the system has also been obtained. Thereafter equilibrium positions of the motion of the system have been obtained.

On the Asymptotic Stability of Discrete Crocodilians Model

The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).

Determining spatial structures of ion crystals by simulated annealing method

Calculating the spatial structures of ion crystals is important in ion-trapped quantum computation. Here we demon- strate that the simulated annealing method is a powerful tool to evaluate the structures of ion crystals. By calculating equilibrium positions of 10 ions under harmonic potential and those of 120 ions under anharmonic potential, both with the standard procedure and simulated annealing method, we find that the standard procedure to evaluate spatial structures is complicated and may be inefficient in some cases, and that the simulated annealing method is more favorable.

On edge dislocation in a multilayered laminate

We investigate the elastic field induced by an edge dislocation in a multilayered laminated composite composed of(N—2)thin bonded elastic layers sandwiched between two semi-infinite elastic media.A simple closed-form solution is obtained when all the phases have equal shear modulus but different Poisson's ratios,and when the dislocation is located in the upper semi-infinite phase.The image force acting on the dislocation due to its interaction with the multilayered structure is also derived. Several specific examples are discussed in detail to illustrate the mobility of the edge dislocation. Some interesting behaviors of the dislocation are observed.Our results indicate that it is possible to find at most(N—2)equilibrium positions for the edge dislocation in an N-phase composite structure.

Global attractivity of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays

This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior.By using the theory of functional differential equations,the fluctuation lemma,and the technique of differential inequalities,some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established.In addition,the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.

Numerical study on heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion

Janus particle is a research hotspot due to its novelty and settlement in acid liquid during wastewater treatment.Heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion are numerically investigated based on immersed boundary lattice Boltzmann method.Chemical reaction heat ratio,Damkohler number,Peclet number,and particle number effects on temperature field,concentration field,Janus particle mass reduction,position,and velocity are investigated.The uniform particle has an equilibrium position of about 1/4 times the channel width for two corroded uniform particle settlement processes.The Janus particle horizontal position deviates from the uniform particle equilibrium position due to the force caused by nonuniform buoyancy and particle rotation.When the chemical reaction heat ratio is more than 1,the Janus particle horizontal position is closer to the channel centerline and has a positive deviation.However,the converse trend happens when the chemical reaction heat ratio is less than 1,and the Janus particle horizontal position has a negative deviation.The Janus particle horizontal position deviation magnitude increases with increasing Damkohler number and decreasing Peclet number.The horizontal position deviation phenomenon exists for the single corroded Janus particle and two corroded Janus particle settlement processes.

THE GLOBAL STABILITY OF A COMPETING CHEMOSTAT MODEL WITH DELAYED NUTRIENT RECYCLING

In this paper, by applying the method of Liapunov functionals we study the global stability of the positive equilibrium of a competing chemostat model with delayed nutrient recycling. The sufficient conditions of the global stability (involved in average time delay or not) are obtained.

Qualitative Analysis of a Strongly Coupled Prey-Predator Model

This paper investigates a strongly coupled reaction-diffusion model with Holling-II reaction function in a bounded domain with homogeneous Neumann boundary condition. The sufficient condition for the existence and non-existence of the non-constant positive solutions are obtained. Moreover, we prove that the nonlinear diffusion terms can create non-constant positive equilibrium solutions when the corresponding model without nonlinear diffusion term fails.

Dynamical behaviour of stochastic competition system with harvest and Lévy jumps

This paper studies stochastic competition system with harvest which is subject to Lévy jumps.Firstly,it is obtained that the system has a unique global positive solution with any positive initial value.Then stochastic extinction of population is established due to Lévy jumps under a simple condition.Sufficient condition for persistence has been derived around positive equilibrium of the population.Finally,some numerical simulations are also introduced to illustrate the main results.

ATTRACTIVE BEHAVIOR OF SOLUTIONS OF A NONLINEAR HIGHER ORDER DIFFERENCE EQUATIONS

In this paper, we study the global attractivity of solutions of higher order nonlinear difference equation xn＋a=f（xn＋ι-1,xn＋ι-2,…,xn,xn-1）,n=0,1,2,…,where f is a continuous, positive, decreasing function on [0, ＋∞）^ι＋1／{（0,…, 0）}. We extend some known global behavior of the solutions of nonlinear higher order difference equations.