On Chaotic Dynamics Of Complex Networks And Systems

Chaotic behavior is the pseudo-random behavior in deterministic nonlinear system.Control and anti-control of chaotic system has been a hot focus of research in nonlinearsystem theory and application. Due to the ubiquity of chaos and some useful applicationsin non-classical cases, the study on the control and anti-control of chaos is of significantimportance. Just like the ubiquity of chaotic system, complex networks can also be usedto model and characterize many natural and man-made networks. However, theanti-control problem of chaos in the settings of complex network has never beeninvestigated. This thesis studied the problem of chaotification of complex networks.What’s more, the thesis also talked about novel chaotic attractors in Hopfield neuralnetworks and some three dimensional systems. In summary, the main results include:Chaotification of complex networks is studied via feedback control, and sufficientand necessary results are given.Chaotification of complex networks is investigated via impulsive control, and therelationship of impulse interval and control gain is presented to guarantee all the states ofevery node in complex networks are chaotic.A novel chaotic attractor in Hopfield neural network is found. The existence ofhorseshoe is rigorously verified by the computer aided simulation, and then the synthesisof chaotic attractor is studied via parameter switching.The concept multichaos is given and two concrete examples are given to clarify thephenomenon of multichaos.