# American Institute of Mathematical Sciences

2015, 2015(special): 652-659. doi: 10.3934/proc.2015.0652

## On global dynamics in a multi-dimensional discrete map

 1 Department of Mathematics, Pennsylvania State University, PO Box PSU, Lehman, PA 18627, United States

Received  September 2014 Revised  October 2015 Published  November 2015

We derive preliminary results on global dynamics of the multi-dimensional discrete map $$F:\; (x_1,x_2,\dots,x_{k-1},x_k)\mapsto (x_1+af(x_k),x_1,x_2,\dots,x_{k-1})$$ where the continuous real-valued function $f$ is one-sided bounded and satisfying the negative feedback condition, $x\cdot f(x)<0, x\ne0$, $a$ is a positive parameter. We show the existence of a compact global attractor for map $F$, and derive a condition for the global attractivity of the zero fixed point.
Citation: Anatoli F. Ivanov. On global dynamics in a multi-dimensional discrete map. Conference Publications, 2015, 2015 (special) : 652-659. doi: 10.3934/proc.2015.0652
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