[4] Reviewer Henry Ricardo writes that the book is "more suitable to an undergraduate course" than its alternatives, despite being less in-depth, because of its greater accessibility and connection to application areas. The Beverton–Holt model is widely applied in the assessment of species biomass and fitted to experimental data to obtain a suitable range of parameter values. In this paper, we consider the explicit solution of the following system of nonlinear rational difference equations: x[n+1]=x[n−1]/(x[n−1]+r) , y[n+1]=x[n−1]y[n]/(x[n−1]y[n]+r) , with initial conditions x[−1] , x[0] and y[0] , which are arbitrary positive real numbers. For a better shopping experience, please upgrade now. Furthermore, we derive some important inequalities and directly utilize the use of a well-known Young’s inequality for some of the oscillatory results. The acoustic dispersion properties of monodimensional waveguide filters can be assessed by means of the simple prototypical mechanical system made of an infinite stack of periodic massive blocks, connected to each other by elastic joints. Forest models and sufficient information for predictions are important for ensuring efficient afforestation activities and sustainable forest development. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. By imposing repetition condition on this equation, we reach to a significant finding named Simple and Compound Motion Cycles as general solutions of steady walking. To make the presentation concrete and appealing, the programming x(n+1)=A(n)x(n)+D(n)x(n-h)+g(n,x(n))+\sum_{s=n-h}^{n}B(n,s)f(s,x(s)). In this article, we discuss the effect of this memory property on solutions of nabla fractional difference equations associated with initial and boundary value problems. Our equation for a choice of parameter is diconjugate, and for a different choice can have positive and oscillatory solutions at the same time. The method produces the generating function of the partition functions of systems of all sizes. The difference equation and discrete expression of differential equations belong to the field of nonlinear analysis in mathematics and can elucidate highly complex properties through a simple defined recursive relationship [17][18][19]. We study the properties of eigenvalues and eigenvectors of the generator T_{n,ε,ϕ} of the τ_{ε,ϕ} algebra. The results show that expressing the logistic map in terms of complex variables leads to more distinguished behaviors, which could not be achieved in the logistic map with real variables. We are considered with the discrete nonlinear two-point boundary value problem at resonance: Lu(j)=ν1u(j)+g(u(j))-e(j),j∈T,u(0)=u(T+1)=0,(P)where Lu(j)={-▵2u(j-1)+b(j)Δu(j)+a0(j)u(j),j∈T,0,j∈{0,T+1},b, e: T→ R, a: T→ [0 , ∞) , ν 1 is the principal eigenvalue of L. We show that there exists a constant d> ν 1 , depending only on b and a, such that if limsup|ξ|→∞g(ξ)ξ