This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n − 2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.

The problem of computing periodic solutions can be expressed as a boundary value problem and solved numerically via piecewise collocation.Here, we extend to renewal equations the corresponding method for retarded funcional dierential equations in [K.Engelborghs et al.,

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period-doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge-based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long-term chaotic behavior over a broad range of parameters.

This article deals with mathematical modeling and simulation of heat transfer in tissue under periodic boundary condition using nonlinear dual-phase-lag-bioheat-transfer (DPLBHT). We have taken the temperature dependent blood perfusion and metabolic heat source as exponent variation in nonlinear DPLBHT model, both are experimentally validated function of temperature. In this article we applied finite difference method and Runge–Kutta (4,5) scheme to solve nonlinear problem. In particular case the exact solution is obtained and compared with numerical scheme and both are in good agreement. Effect of different parameters are discussed in detail such as blood perfusion rate, dimensionless heat source parameters, relaxation, and thermalization time on dimensionless temperature. The whole article is analyzed in dimensionless form.

In the present article, the periodic solutions of the N-body with quasi-homogeneous potential in the Sitnikov sense by applying the multiple methods of scale (MMS) and Lindstedt–Poincaré (LP) technique are obtained. However, these methods are used to find the approximate periodic solutions in the closed form by eliminating the secular terms. In addition of the Newtonian potential and forces, we consider that the big bodies create quasi-homogeneous potentials. We add the inverse cubic corrective term to the inverse square Newtonian law of gravitation, in order to approximate the various phenomena due to the shape of the bodies or the radiation emitting from them. We study the Sitnikov motion in the N-bodies under this consideration. We, further, analyzed the obtain approximate periodic solutions of the Sitnikov motion, for ν = 2 , 7 by using the MMS and LP-method, in closed form. The numerical comparisons are presented in the first and second approximated solutions obtained by using MMS and numerical solutions obtained by LP-method are illustrated graphically. The effect of initial conditions on the solutions of the Sitnikov motion is illustrated graphically obtained by both the techniques. It is observed that the choice of initial conditions plays a crucial role in the numerical and approximate solutions.

Since decades, hazardous chemicals are used to control the growth of carriers (flies, ticks, mites, and so on) in the environment, which are responsible for the spread of many infectious diseases, such as typhoid fever, polio, and some skin infections such as leprosy, and so on. Although these chemicals reduce the carrier population, they also inflict a sizeable harm to nontarget populations, like the human population. In this study, we present a mathematical model to control the carrier population using biological agents, which leads to the control of carrier-dependent infectious diseases. It is assumed that the disease can spread in the human population due to the direct contact between susceptible and infected individuals, but also indirectly through the vector population. The feasibility and stability of the system's equilibria are discussed. The key parameters of the proposed model are identified and their role in the transmission and control of such diseases is discussed. Our findings show that combined actions of two strategies, the biological control of carriers via parasitic wasps that target the immature stage of the flies and any extra exogenous means which eradicate the adult carriers when their population is at low levels, could be an effective and low cost approach to lessen the disease propagation.