11 research outputs found

    Hidden attractors in fundamental problems and engineering models

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    Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

    Hybrid Chaos Synchronization of 3-Cells Cellular Neural Network Attractors via Adaptive Control Method

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    Abstract: In this research work, we first discuss the properties of the 3-cells cellular neural network (CNN) attractor discovered b

    Hybrid Synchronization of the Generalized Lotka-Volterra Three-Species Biological Systems via Adaptive Control

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    Abstract: Since the recent research has shown the importance of biological control in many biological systems appearing in nature, this research paper investigates research in the dynamic and chaotic analysis of the generalized Lotka-Volterra three-species biological system, which was studied b

    A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization and Its Digital Implementation

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    YesIn this paper, a new fractional order chaotic system without equilibrium is proposed, analyti-cally and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigation were used to describe the system dynamical behaviors including, the system equilibria, the chaotic attractors, the bifurcation diagrams and the Lyapunov expo-nents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attrac-tors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive con-trol theory has been developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state varia-bles for the master and slave. Consequently, the update laws of the slave parameters are ob-tained, where the slave parameters are assumed to be uncertain and estimate corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results are obtained by MATLAB and the Arduino Due boards respectively, where a good consistent between the simulation results and the ex-perimental results. indicating that the new fractional order chaotic system is capable of being employed in real-world applications

    Attractors and bifurcations of chaotic systems

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    The hidden bifurcation idea was discovered by the core idea of the Leonov and Kuznetsov method for searching hidden attractors (i.e., homotopy and numerical continuation) differently in order to uncover hidden bifurcations governed by a homotopy parameter ɛ while keeping the numbers of spirals. This idea was first discovered by Menacer et al. In 2016, in the multispiral Chua system, The first part of this thesis is devoted to providing a basic understanding of dynamic systems and chaos, followed by an introduction to the hidden attractors, history, and definitions. An effective procedure for the numerical localization of hidden attractors in multidimensional dynamical systems has been presented by Leonov et Kuznetsov. In this part, we end with the study of hidden attractors in the Chua system. The second part of the analysis consists of first, hidden modalities ofspirals of chaotic attractor via saturated function series and numerical results. Before reaching the asymptotic attractor which possesses an even number of spirals, these latter are generated one after one until they reach their maximum number, matching the value fixed by ɛ. Then, we end up by symmetries in hidden bifurcation routes to multiscroll chaotic attractors generated by saturated function series. The method to find such hidden bifurcation routes (HBR) depends upon two parameters

    Criptografia baseada em caos : aplicação usando um sistema hipercaótico

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    Trabalho de conclusão de curso (graduação)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2019.Neste trabalho se propõe um esquema para telecomunicação segura baseado na sincroni zação de um sistema nonodimensional hipercaotico e analise de Lyapunov. Ao contrário da maioria dos esquemas usualmente encontrados na literatura, o esquema proposto requer apenas que o controle atue em uma das equações de estado do sistema escravo. Foi verificada mate maticamente a convergência do erro de sincronização para um conjunto compacto arbitrário, permitindo-se obter um erro convergente a uma vizinhança da origem. Com um circuito caótico transmissor (ou mestre) codifica-se o sinal (ou mensagem) e com outro circuito caótico receptor (ou escravo) recupera-se a mensagem. O esquema proposto tem como vantagens ser robusto contra perturbações (internas e externas) e ser estruturalmente simples, quando comparado com as propostas existentes na literatura, o que é importante, uma vez que leva a redução de custos quando implementado utilizando eletrônica analógica. Para validar a robustez e simplicidade do esquema proposto, simulações computacionais utilizando software MATLAB/Simulink foram realizadas.This work proposes a scheme for secure telecommunication based on the synchronization of a hyperchaotic system and Lyapunov analysis. Unlike most schemes usually found in the literature, the proposed scheme only requires that the control act on one of the slave state equa tions. The convergence of the synchronization error to an arbitrary compact set was verified mathematically, allowing a convergent error to be arbitrarily small neighborhood of the origin. With a transmitting (or master) chaotic circuit the signal (or message) is encoded and with another receiving (or slave) chaotic circuit the message is retrieved. The proposed scheme has the advantages of being robust against disturbances (internal and external) and being structu rally simple when compared to the existing proposals in the literature, which is important as it leads to cost savings when implemented using analog electronics. To validate the robust ness and simplicity of the proposed scheme, computer simulations using MATLAB/Simulink software were performed
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