Geometric Stability Conditions for Higher Order Difference Equations
Copyright policy )Geometric Stability Conditions for Higher Order Difference Equations
The author considers the higher order autonomous difference equation \[ x_n= f(x_{n-1}, \dots, x_{n-m}),\;n=1,2,3, \dots \tag{1} \] where the order \(m\) is a fixed positive integer larger than 1. Under some suitable conditions on \(f\) the author discusses the asymptotic stability, the exponential stability relative to the invariant sets, and the instability with the aid of a general class of sets for equation (1). Examples are given to illustrate the results.
- Virginia Commonwealth University United States
asymptotic stability, instability, Stability of difference equations, exponential stability, Applied Mathematics, geometric stability, higher order autonomous difference equation, Analysis
asymptotic stability, instability, Stability of difference equations, exponential stability, Applied Mathematics, geometric stability, higher order autonomous difference equation, Analysis
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