12 research outputs found

    Constructing multiwing attractors from a robust chaotic system with non-hyperbolic equilibrium points

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    We investigate a three-dimensional (3D) robust chaotic system which only holds two nonhyperbolic equilibrium points, and finds the complex dynamical behaviour of position modulation beyond amplitude modulation. To extend the application of this chaotic system, we initiate a novel methodology to construct multiwing chaotic attractors by modifying the position and amplitude parameters. Moreover, the signal amplitude, range and distance of the generated multiwings can be easily adjusted by using the control parameters, which enable us to enhance the potential application in chaotic cryptography and secure communication. The effectiveness of the theoretical analyses is confirmed by numerical simulations. Particularly, the multiwing attractor is physically realized by using DSP (digital signal processor) chip

    On new chaotic and hyperchaotic systems: A literature survey

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    This paper provides a thorough survey of new chaotic and hyperchaotic systems. An analysis of the dynamic behavior of these complex systems is presented by pointing out their originality and elementary characteristics. Recently, such systems have been increasingly used in various fields such as secure communication, encryption and finance and so on. In practice, each field requires specific performances with peculiar complexity. A particular classification is then proposed in this paper based on the Lyapunov exponent, the equilibriums points and the attractor forms

    Hybrid Synchronization of n-scroll Chaotic Chua Circuits using Adaptive Backstepping Control Design with Recursive Feedback

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    ABSTRACT In this paper, the hybrid synchronization is investigated for n-scroll chaotic Chua circui

    Control of a novel chaotic fractional order system using a state feedback technique

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    We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the Routh-Hurwitz and the Matignon stability criteria, we analyze the novel chaotic fractional order system and propose a control methodology that is better than the nonlinear counterparts available in the literature, in the sense of simplicity of implementation and analysis. A scalar control input that excites only one of the states is proposed, and sufficient conditions for the controller gain to stabilize the unstable equilibrium points derived. Numerical simulations confirm the theoretical analysis. 漏 2013 Elsevier Ltd. All rights reserved

    Synchronization of Monostatic Radar Using a Time-Delayed Chaos-Based FM Waveform

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    There is no doubt that chaotic systems are still attractive issues in various radar applications and communication systems. In this paper, we present a new 0.3 GHz mono-static microwave chaotic radar. It includes a chaotic system based on a time-delay to generate and process frequency modulated (FM) waveforms. Such a radar is designed to extract high-resolution information from the targets. To generate a continuous FM signal, the chaotic signal is first modulated using the voltage control oscillator (VCO). Next, the correct value for the loop gain (G) is carefully set when utilizing the Phase-Locked Loop (PLL) at the receiver, so that the instantaneous frequency that reflects a chaotic state variable can be reliably recovered. In this system, the PLL synchronization and radar correlation are enough to recover the echo signal and detect the target. The finding indicates that the system can be implemented with no need to use the complete self-synchronization or complex projective synchronization schemes as compared to the existing chaotic radar systems. The simulation results show that the short-time cross-correlation of the transmitted and reconstructed waveforms is good and satisfactory to detect the target under various signal-to-noise ratio (SNR) levels and with less complexity in the design

    Fractional order chaotic systems and their electronic design

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    "Con el desarrollo del c谩lculo fraccionario y la teor铆a del caos, los sistemas ca贸ticos de orden fraccionario se han convertido en una forma 煤til de evaluar las caracter铆sticas de los sistemas din谩micos. En esta direcci贸n, esta tesis es principalmente relacionada, es decir, en el estudio de sistemas ca贸ticos de orden fraccionario, basado en sistemas disipativos de inestables, un sistema disipativo de inestable de orden fraccionario es propuesto. Algunas propiedades din谩micas como puntos de equilibrio, exponentes de Lyapunov, diagramas de bifurcaci贸n y comportamientos din谩micos ca贸ticos del sistema ca贸tico de orden fraccionario son estudiados. Los resultados obtenidos muestran claramente que el sistema discutido presenta un comportamiento ca贸tico. Por medio de considerar la teor铆a del c谩lculo fraccionario y simulaciones num茅ricas, se muestra que el comportamiento ca贸tico existe en el sistema de tres ecuaciones diferenciales de orden fraccionario acopladas, con un orden menor a tres. Estos resultados son validados por la existencia de un exponente positivo de Lyapunov, adem谩s de algunos diagramas de fase. Por otra parte, la presencia de caos es tambi茅n verificada obteniendo la herradura topol贸gica. Dicha prueba topol贸gica garantiza la generaci麓n de caos en el sistema de orden fraccionario propuesto. En orden de verificar la efectividad del sistema propuesto, un circuito electr贸nico es dise帽ado con el fin de sintetizar el sistema ca贸tico de orden fraccionario.""With the development of fractional order calculus and chaos theory, the fractional order chaotic systems have become a useful way to evaluate characteristics of dynamical systems and forecast the trend of complex systems. In this direction, this thesis is primarily concerned with the study of fractional order chaotic systems, based on an unstable dissipative system (UDS), a fractional order unstable dissipative system (FOUDS) is proposed. Dynamical properties, such as equilibrium points, Lyapunov exponents, bifurcation diagrams and phase diagrams of the fractional order chaotic system are studied. The obtained results shown that the fractional order unstable dissipative system has a chaotic behavior. By utilizing the fractional calculus theory and computer simulations, it is found that chaos exists in the fractional order three dimensional system with order less than three. The lowest order to yield chaos in this system is 2.4. The results are validated by the existence of one positive Lyapunov exponent, phase diagrams; Besides, the presence of chaos is also verified obtaining the topological horseshoe. That topological proof guarantees the chaos generation in the proposed fractional order unstable dissipative system. In order to verify the effectiveness of the proposed system, an electronic circuit is designed with the purpose of synthesize the fractional order chaotic system, the fractional order integral is realized with electronic circuit utilizing the synthesis of a fractance circuit. The realization has been done via synthesis as passive RC circuits connected to an operational amplifier. The continuos fractional expansion have been utilized on fractional integration transfer function which has been approximated to integer order rational transfer function considering the Charef Method. The analogue electronics circuits have been simulated using HSPICE.
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