Stability and bifurcation analysis of a class of networked dynamical systems

In this brief, stability and bifurcation in a class of networked dynamical systems are investigated. First, it is shown that, for each member of the family, there is a globally attracting region. Then, the local stability of a particular fixed point (0, 0) is investigated; afterward, it is found that this fixed point is a bifurcation point as a certain system parameter varies. Finally, a family of 3-D dynamical systems is numerically studied, with rich and diverse bifurcating phenomena and geometrically different attractors being revealed. It is also observed that the geometry of attractors undergoes continuous deformation as a function of a certain parameter.