Spatio-temporal statistical models are ubiquitous in the environmental sciences. Often the underlying spatiotemporal process can be written as a hierarchical state-space process that utilizes prior understanding of the physical process to formulate models for the state transition. In situations with complicated dynamics, such as wave propagation, or population growth and dispersal models, param...

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal i.e....

In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor with a basin under certain conditions....

By using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation ∆ [p(t)∆u(t − 1)] + f(t, u(t)) = 0 has at least one homoclinic orbit, where t ∈ Z, u ∈ R.

The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuousand discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized sy...

We consider the higher-order nonlinear difference equation xn 1 α xn / A Bxn xn−k , n 0, 1, . . ., where parameters are positive real numbers and initial conditions x−k, . . . , x0 are nonnegative real numbers, k ≥ 2. We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the uniq...

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation xn+1 = Axn + xn−1 B + xn−1 , n = 0, 1, · · · , where (xn) is a sequence of positive fuzzy number, A,B are positive fuzzy numbers and the initial conditions x−1, x0 are positive fuzzy numbers.

The existence of bounded nonoscillatory solutions of a higher-order nonlinear neutral delay difference equationΔ akn · · ·Δ a2nΔ a1nΔ xn bnxn−d f n, xn−r1n , xn−r2n , . . . , xn−rsn 0, n ≥ n0, where n0 ≥ 0, d > 0, k > 0, and s > 0 are integers, {ain}n≥n0 i 1, 2, . . . , k and {bn}n≥n0 are real sequences, ⋃s j 1{rjn}n≥n0 ⊆ Z, and f : {n : n ≥ n0} × R → R is a mapping, is studied. Some sufficient...

We prove a difference equation analogue of the decay-of-mass result for the nonlinear parabolic equation ut = ∆u+ μ|∇u| when μ < 0, and a new growth result when μ > 0.

and Applied Analysis 3 Let l∞ β denote the Banach space of all bounded sequences in Zβ with norm ‖x‖ sup n∈Zβ |xn| for x {xn}n∈Zβ ∈ l∞ β , B d,D { x {xn}n∈Zβ ∈ l∞ β : ‖x − d‖ ≤ D } for d {d}n∈Zβ ∈ l∞ β , D > 0 2.2 represent the closed ball centered at d and with radius D in l∞ β . By a solution of 1.1 , we mean a sequence {xn}n∈Zβ with a positive integer T ≥ n0 τ |β| such that 1.1 is satisfied ...