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The aim of this study is to identify sugareane genotypes that eombine high yield and stability aeross environments to identify best potential eultivars of sugareane for a region during the years 201718 and 2018-19. Fourteen sugareane genotypes under varietal development programme of Sugareane Research Institute, Faisalabad were evaluated in two different loeations of northern region in Punjab, Pakistan for their yield response and stability in that eeology, The research trials was earried out in randomized eomplete bloek design with three replieates. The sugareane genotype S2005-US-54 stand best performer by aehieving eane yield of 122 t/ha and sugar yield of 15.52 t/ha at Bhalwal, while sugareane genotype CPF-253 and CPF-252 produeed high eane yield of 129 t/ha, 125 t/ha and sugar yield of 16.69 t/ha, 15.25 t/ha at Chelianwala respeetively. The adaptability and stability studies of fourteen genotypes eoneluded that CPF-253, S2005-US-54, CPF-252 produeed the highest eane yield of 123.5 t/ha, 121.5 t/ha, 115t/ha respeetively and most of the produetive genotypes being high yielding ability was best suited for planting in northern agro-eeologies in Punjab. [ABSTRACT FROM AUTHOR]

The boundedness nature and persistence, global and local behavior, and rate of convergence of positive solutions of a second-order system of exponential difference equations, is investigated in this work. Where the parameters A , B , C , α , β , γ , δ , η , and ξ are constants that are positive, and the initials U − 1 , U 0 , V − 1 , V 0 , W − 1 , and W 0 are non-negative real numbers. Some examples are provided to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

This research manifesto has a comprehensive discussion of the global dynamics of an achievable discrete-time two predators and one prey Lotka–Volterra model in three dimensions, i.e., in the space R 3 . In some assertive parametric circumstances, the discrete-time model has eight equilibrium points among which one is a special or unique positive equilibrium point. We have also investigated the local and global behavior of equilibrium points of an achievable three-dimensional discrete-time two predators and one prey Lotka–Volterra model. The conversion of a continuous-type model into its discrete counterpart model has been completed by adopting a dynamically consistent nonstandard difference scheme with the end goal that the equilibrium points are conserved in twin cases. The difficulty lies in how to find all fixed points O , P , Q , R , S , T , U , V and the Jacobian matrix and its characteristic polynomial at the unique positive fixed point. For that purpose, we use Mathematica software to find the equilibrium points and all of the Jacobian matrices at those equilibrium points. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of the obtained system about all of its equilibrium points. The discrete Lotka–Volterra model in three dimensions is given by system (3), where parameters α , β , γ , δ , ζ , η , μ , ε , υ , ρ , σ , ω ∈ R + and initial conditions x 0 , y 0 , z 0 are positive real numbers. Additionally, the rate of convergence of a solution that converges to a unique positive equilibrium point is discussed. To represent theoretical perceptions, some numerical debates are introduced, including phase portraits. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation ... where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-l + b + cxn-k/dxn-s + exn-t, n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants:Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-l + b + cxn-k/dxn-s + exn-t, n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants:Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-1l + . . ., n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-1l + bxn-k + cxn-s/d + exn-t , n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. [ABSTRACT FROM AUTHOR]