Synchronization of complex networks of identical and nonidentical chaotic systems via model-matching control

Abstract

In this work, a synchronization scheme for networks of complex systems is presented. The proposed synchronization scheme uses a control law obtained with some definitions from graph theory and solving the Model-Matching Problem for complex networks. In particular, Rössler, Chen, Lorenz and Lü chaotic systems are used as complex chaotic systems into complex networks. Particular cases with regular and irregular networks of six identical chaotic systems are implemented, with some well-known topologies as star and ring small-world, and tree topologies. Highlighting, the obtained control law is applied to synchronize an irregular network of six different chaotic systems in a tree topology. The usefulness and advantages of the proposed synchronization scheme are highlighted performing numerical simulations of the chaotic complex networks.

Master-slave synchronization in the Rayleigh and Duffing oscillators via elastic and dissipative couplings

“…This system exhibits complex bifurcation structures with an important number of periodic states, a chaotic region and islands of periodic states, showing, in addition, transitions from chaos to stable states. The dynamics based on identical or distinct linear oscillators presenting the same kind of attractors is still under study [8,9]. Nevertheless, the dynamics of these systems in states of different attractors is of current interest and it could give rise to important information.…”

Encrypted Physical Layer Communications Using Synchronized Hyperchaotic Maps

“…Thus, unlike the above-mentioned RNG-based digital encryption methods, here we utilize the extreme parameter sensitivity of chaotic systems as private encryption keys for data communications. This approach also results in a simple enrollment process: security keys are shared simply by using a pair of chaotic systems with the same set of parameters, in which case generalized synchronization methods [10], [11] can be applied to guarantee successful data decryption. The effects of unavoidable parameter mismatches can also be minimized using recently-proposed adaptive synchronization methods [4], thus improving robustness.…”

Controlling synchronization in a complex network of nonlinear oscillators via feedback linearisation and H∞-control

“…Commonly, these techniques relate to a single specific application study, hindering the scope of application of the proposed methods for a general class of networkcoupled systems, hence limiting any results/conclusions to the specific case study presented. A step towards a 'general' framework for complete synchronization has been taken in López-Mancilla et al [16] , via a model-matching approach. Nonetheless, López-Mancilla et al [16] inherently requires perfect knowledge of the dynamics of the network, which is virtually always unavailable in a realistic scenario, where unmodelled dynamics are ubiquitous.…”

“…A step towards a 'general' framework for complete synchronization has been taken in López-Mancilla et al [16] , via a model-matching approach. Nonetheless, López-Mancilla et al [16] inherently requires perfect knowledge of the dynamics of the network, which is virtually always unavailable in a realistic scenario, where unmodelled dynamics are ubiquitous.…”