Systems Of Higher-order Difference Equations Research Articles

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

This paper aims to derive analytical expressions for solutions of fractional bidimensional systems of difference equations with higher-order terms under specific parametric conditions. Additionally, formulations of solutions for one-dimensional equations derived from these systems are explored. Furthermore, rigorous proof is provided for the local stability of the unique positive equilibrium point of the proposed systems. The theoretical findings are validated through numerical examples using MATLAB, facilitating graphical illustrations of the results.

The Solution of a System of Higher-Order Difference Equations in Terms of Balancing Numbers

In this paper, we are interested in the closed-form solution of the following system of nonlinear difference equations of higher order,un+1 = 1/34-vn-m , vn+1 = 1/34-un-m, n, m ∈ N0,and the initial values u-j and v-j , j∈{0, 1, ..., m} are real numbers do not equal 34. We show that the solutions of this system are associated with Balancing numbers. As consequence, these solutions are also associated with Pell numbers, Pell-Lucas numbers, and Lucas-Balancing numbers. It is shown that the global stability of positive solutions of this system holds. Our results are illustrated via numerical examples.

Stability of higher-order discrete-time Lur'e systems

We consider discrete-time Lur'e systems obtained by applying nonlinear feedback to a system of higher-order difference equations (ARMA models). The ARMA model relates the inputs and outputs of the linear system and does not involve any internal or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability, a concept which is very much reminiscent of input-to-state stability.

Form and Periodicity of Solutions of Some Systems of Higher-Order Difference Equations

Form and Periodicity of Solutions of Some Systems of Higher-Order Difference Equations

Further results on fixed-sign solutions for a system of higher-order difference equations

We consider the following system of n th order boundary value problems: where u i(k) = (u i(k), Δu i(k),…, Δ n−2u i(k)), 1 ≤ i ≤ m. Criteria are offered for the existence of single and double fixed-sign solutions of the system. We also include examples to illustrate the importance of the results obtained.

Convergence to equilibria in recurrence equations

In this paper, we deal with linear and nonlinear perturbations of first-order recurrence systems with constant coefficients having infinitely many equilibria. We give sufficient conditions for the asymptotic constancy of the solutions of the perturbed equation. As a consequence of our main theorem, we obtain sufficient conditions for systems of higher-order difference equations to have asymptotic equilibrium.

A closed-form solution of singular regular higher-order difference initial and boundary value problems

In this paper existence conditions and a closed-form expression for solutions of coupled singular systems of higher-order difference equations are given. The approach avoids the computational drawbacks derived from the standard approach based on the consideration of an equivalent first-order system.