Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and Dynamics of Complex Order Fractional Difference Equations   We extend the definition of $n$-dimensional difference equations to complex
order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems
defined by an $n$-dimensional matrix $A$ and derive conditions for the
stability of equilibrium points for linear systems. For the one-dimensional
case where $A =\lambda \in \mathbb {C}$, we find that the stability region, if
any is enclosed by a boundary curve and we obtain a parametric equation for the
same. Furthermore, we find that there is no stable region if this parametric
curve is self-intersecting. Even for $ \lambda \in \mathbb{R} $, the solutions
can be complex and dynamics in one-dimension is richer than the case for $
\alpha\in \mathbb{R} $. These results can be extended to $n$-dimensions. For
nonlinear systems, we observe that the stability of the linearized system
determines the stability of the equilibrium point.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg