论文标题
分数耦合地图晶格的固定点的稳定性分析
Stability analysis of fixed point of fractional-order coupled map lattices
论文作者
论文摘要
我们研究线性分数耦合地图晶格（CML）的同步定点状态的稳定性。我们观察到连通矩阵的特征值决定了整数cml的稳定性。这些特征值可以在某些情况下精确确定。我们在使用循环矩阵理论的一维晶格中发现了具有翻译不变耦合的确切边界。这可以扩展到任何有限的维度。可以针对非线性耦合分数图的同步固定点进行类似的分析，其中Jacobian矩阵的特征值起着相同的作用。该分析是通用的，并表明连通性矩阵的特征值在同步固定点的稳定性分析中起着关键作用，即使在耦合的分数图中也是如此。
We study the stability of synchronized fixed-point state for linear fractional-order coupled map lattice(CML). We observe that the eigenvalues of the connectivity matrix determine the stability as for integer-order CML. These eigenvalues can be determined exactly in certain cases. We find exact bounds in one-dimensional lattice with translationally invariant coupling using the theory of circulant matrices. This can be extended to any finite dimension. Similar analysis can be carried out for the synchronized fixed point of nonlinear coupled fractional maps where eigenvalues of the Jacobian matrix play the same role. The analysis is generic and demonstrates that the eigenvalues of connectivity matrix play a pivotal role in stability analysis of synchronized fixed point even in coupled fractional maps.
