A particular system of two-dimensional Lotka-Volterra maps, $T_a:(x^{\prime },y^{\prime })=(x(a-x-y),xy),$ unfolding a map originally proposed by Sharkovsky for $a=4,$ is considered. We show the routes to chaos leading to the dynamics of map $T_4.$ For map $T_4$ we show that even if the stable set of the origin $O$ includes a set dense in an invariant area, the only homoclinic points of $O$ belong to the $x-$axis, as well as the cycles leading to heteroclinic connections, while many internal cycles are snap-back repellers. We also show that a particular 6-cycle known analytically for map $T_4$ exists, and is known explicitly in closed form, for any $a\in (3,4]$ appearing at a supercritical Neimark-Sacker bifurcation of the positive fixed point. Moreover, we show the existence of infinitely many $k-$cycles on the $x-$axis (for any $k>3$), which are topological attractors of map $T_a$ for $a\in (3.96,4)$ and saddle cycles transversely attracting at $a=4$.

二维Lotka-Volterra地图的特定系统， ${Ť}_{\mathrm{一种}}：（X^{\prime }，{ÿ}^{\prime }）=（X（\mathrm{一种}-X-ÿ），Xÿ），$ 展开一张由Sharkovsky最初提出的用于 $\mathrm{一种}=4，$被认为。我们展示了导致混乱的路线，从而导致了地图的动态变化${Ť}_4。$ 对于地图 ${Ť}_4$ 我们证明即使原点的稳定集 $Ø$ 包括在不变区域内密集的集合， $Ø$ 属于 $X-$轴，以及导致异斜面连接的循环，而许多内部循环是回弹排斥器。我们还显示了一个特定的6周期，它在分析上已知为map${Ť}_4$ 存在，并且对于任何 $\mathrm{一种}\in （3，4]$出现在正定点的超临界Neimark-Sacker分叉处。而且，我们证明了无限多的存在$ķ-$上的循环 $X-$轴（对于任何 $ķ>3$），它们是地图的拓扑吸引子 ${Ť}_{\mathrm{一种}}$ 为了 $\mathrm{一种}\in （3.96，4）$ 和马鞍周期横向吸引 $\mathrm{一种}=4$。