Grazing Analysis for Synchronization of chaotic hybrid systems

International audienceIn this paper, a Grazing bifurcation analysis is proposed and a way to chaos is presented. Moreover, based on this analysis an observer design for the synchronization of chaotic hybrid system is given

Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3D master chaotic system and 4D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein

Using discrete-time hyperchaotic-based asymmetric encryption and decryption keys for secure signal transmission

In this paper, a framework for the synchronization of two non-identical discrete-time hyperchaotic systems, namely the 3D Baier-Klein and the 3D Hitzel-Zele maps, based on the use of hybrid output feedback concept and aggregation techniques, is employed to design a two-channel secure communication system. New sufficient conditions for synchronization are obtained by the use of Borne and Gentina practical criterion for stabilization study associated to the forced arrow form matrix for system description. The efficiency of the proposed approach to confidentially recover the transmitted message signal is shown via an application to the hyperchaotic Baier-Klein and Hitzel-Zele systems, considered as generators of asymmetric encryption and decryption keys

Cluster synchronization in networks of coupled non-identical dynamical systems

In this paper, we study cluster synchronization in networks of coupled non-identical dynamical systems. The vertices in the same cluster have the same dynamics of uncoupled node system but the uncoupled node systems in different clusters are different. We present conditions guaranteeing cluster synchronization and investigate the relation between cluster synchronization and the unweighted graph topology. We indicate that two condition play key roles for cluster synchronization: the common inter-cluster coupling condition and the intra-cluster communication. From the latter one, we interpret the two well-known cluster synchronization schemes: self-organization and driving, by whether the edges of communication paths lie at inter or intra-cluster. By this way, we classify clusters according to whether the set of edges inter- or intra-cluster edges are removable if wanting to keep the communication between pairs of vertices in the same cluster. Also, we propose adaptive feedback algorithms on the weights of the underlying graph, which can synchronize any bi-directed networks satisfying the two conditions above. We also give several numerical examples to illustrate the theoretical results

Multiobjective synchronization of coupled systems

Copyright @ 2011 American Institute of PhysicsSynchronization of coupled chaotic systems has been a subject of great interest and importance, in theory but also various fields of application, such as secure communication and neuroscience. Recently, based on stability theory, synchronization of coupled chaotic systems by designing appropriate coupling has been widely investigated. However, almost all the available results have been focusing on ensuring the synchronization of coupled chaotic systems with as small coupling strengths as possible. In this contribution, we study multiobjective synchronization of coupled chaotic systems by considering two objectives in parallel, i. e., minimizing optimization of coupling strength and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach. The constraints on the coupling form are also investigated by formulating the problem into a multiobjective constraint problem. We find that the proposed evolutionary method can outperform conventional adaptive strategy in several respects. The results presented in this paper can be extended into nonlinear time-series analysis, synchronization of complex networks and have various applications

Chaos-based communication scheme using proportional and proportional-integral observers

In this paper, we propose a new chaos-based communication scheme using the observers. The novelty lies in the masking procedure that is employed to hide the confidential information using the chaotic oscillator. We use a combination of the addition and inclusion methods to mask the information. The performance of two observers, the proportional observer (P-observer) and the proportional integral observer (PI-observer) is compared that are employed as receivers for the proposed communication scheme. We show that the P-observer is not suitable scheme since it imposes unpractical constraints on the messages to be transmitted. On the other hand, we show that the PI-observer is the better solution because it allows greater flexibility in choosing the gains of the observer and does not impose any unpractical restrictions on the message

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial-linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks and find both the existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure