Generalized projective series synchronization between chaotic systems and its application

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Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems

Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme

Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders

The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works

Modified projective synchronization of fractional-order hyperchaotic memristor-based Chua’s circuit

This paper investigates the modified projective synchronization (MPS) between two hyperchaotic memristor-based Chua circuits modeled by two nonlinear integer-order and fractional-order systems. First, a hyperchaotic memristor-based Chua circuit is suggested, and its dynamics are explored using different tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams. Another interesting property of this circuit was the coexistence of attractors and the appearance of mixed-mode oscillations. It has been shown that one can achieve MPS with integer-order and incommensurate fractional-order memristor-based Chua circuits. Finally, examples of numerical simulation are presented, showing that the theoretical results are in good agreement with the numerical ones

Active backstepping control of combined projective synchronization among different nonlinear systems

In this article, the authors have studied combination projective synchronization using active backstepping method. The main contribution of this effort is realization of the projective synchronization between two drive systems and one response system. We relax some limitations of previous work, where only combination complete synchronization has been investigated. According to Lyapunov stability theory and active backstepping design method, the corresponding controllers are designed to observe combination projective synchronization among three different classical chaotic systems, i.e. the Lorenz system, Rossler system and € Chen system. The numerical simulation examples verify the effectiveness of the theoretical analysis. Combination projective synchronization has stronger anti-attack ability and antitranslated ability than the normal projective synchronization scheme realized by one drive and one response system in secure communication

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed