Abstract
Our aim is to investigate the global behavior of the following fourth‐order rational difference equation: x n +1 = ( x n x n −2 x n −3 + x n + x n −2 + x n −3 + a )/( x n x n −2 + x n x n −3 + x n −2 x n −3 + 1 + a ), n = 0, 1, 2, … where a ∈ [0, ∞ ) and the initial values x −3 , x −2 , x −1 , x 0 ∈ (0, ∞ ). To verify that the positive equilibrium point of the equation is globally asymptotically stable, we used the rule of the successive lengths of positive and negative semicycles of nontrivial solutions of the aforementioned equation.
Keywords
Mathematics
Order (exchange)
Stability (learning theory)
Stability theory
Combinatorics
Equilibrium point
Mathematical analysis
Mathematical physics
Physics
Differential equation
Quantum mechanics
Subject Areas
Mathematical and Theoretical Epidemiology and Ecology Models
·Public Health, Environmental and Occupational Health ·Health Sciences
Nonlinear Differential Equations Analysis
·Applied Mathematics ·Physical Sciences
Fractional Differential Equations Solutions
·Modeling and Simulation ·Physical Sciences
Citations by Year
2022: 1
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