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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Issue 11 • Date Nov 1993

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Displaying Results 1 - 15 of 15
  • Generation of n-double scrolls (n=1, 2, 3, 4,…)

    Publication Year: 1993 , Page(s): 861 - 867
    Cited by:  Papers (35)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (444 KB)  

    Chua's double scroll is probably the best known and most extensively studied example of chaotic behaviour generated by electrical circuits. It is illustrated in this paper that by modifying the characteristic of the nonlinear resistor with additional break points even more “complicated” attractors can be obtained, called n-double scrolls (n=1, 2, 3, 4,…). The new circuit can be ... View full abstract»

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  • Controlling Chua's global unfolding circuit family

    Publication Year: 1993 , Page(s): 829 - 832
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (268 KB)  

    The self-unified and conventional feedback control strategy developed by the present author and his colleagues for the control of chaotic dynamical systems is extended from the Chua's circuit to its global unfolding, driving the circuit dynamics from chaotic attractors to any desirable trajectories such as unstable limit cycles. A simple and realistic sufficient condition for such controllability ... View full abstract»

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  • Dynamic phenomena in chain interconnections of Chua's circuits

    Publication Year: 1993 , Page(s): 868 - 871
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (292 KB)  

    Dynamic phenomena in long chain interconnections of Chua's chaotic circuits are studied. We show via numerical simulations that a large variety of behavior is typically encountered in such systems. Most interesting observations include transmission delay of chaotic “waves”, disorganized propagation, synchronized states, and “chaotic interference”. Results of first laborator... View full abstract»

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  • Derivative control of the steady state in Chua's circuit driven in the chaotic region

    Publication Year: 1993 , Page(s): 833 - 835
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (228 KB)  

    Experimentally demonstrates that Chua's circuit, operating in the double-scroll chaotic regime, may be brought to either of the two unstable, stationary state fixed points by means of derivative control View full abstract»

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  • Synthesis of higher dimensional Chua circuits

    Publication Year: 1993 , Page(s): 854 - 860
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (496 KB)  

    In this paper, we present a universal method to design n-dimensional piecewise linear circuits. These circuits are described by a system of differential equation associated with a piecewise linear continuous vector-field in the n-dimensional state-space, which consists of two different linear regions. The circuits contain only two-terminal elements, one piecewise linear resistor and a number of li... View full abstract»

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  • Using chaos to broaden the capture range of a phase-locked loop

    Publication Year: 1993 , Page(s): 808 - 818
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (944 KB)  

    Phase-space trajectories on a chaotic attractor densely cover a set of nonzero measures, making all points in that set reachable from any initial condition in its basin of attraction. Moreover, the size, shape, and position of the attractor are affected by changes in system parameters, following certain highly characteristic patterns. These properties have been used, in simulations, to broaden the... View full abstract»

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  • Generalizations of the Chua equations

    Publication Year: 1993 , Page(s): 878 - 884
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (536 KB)  

    We present two generalizations of the equations governing Chua's circuit. In the type-I generalization of Chua's equations we use a 2-D autonomous flow as a component in a 3-D autonomous flow in such a way that the resulting equations will have double-scroll attractors similar to those observed experimentally in Chua's circuit. The value of this generalization is that (1) it provides a building bl... View full abstract»

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  • A circuit for real-time horseshoe visualization

    Publication Year: 1993 , Page(s): 841 - 842
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (152 KB)  

    Describes a circuit for the visualization of Poincare return maps of dynamic systems. This circuit is successfully applied to a nonautonomous electrical circuit, which exhibits chaos View full abstract»

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  • Spiral waves on a 2-D array of nonlinear circuits

    Publication Year: 1993 , Page(s): 872 - 877
    Cited by:  Papers (31)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (536 KB)  

    Spatio-temporal patterns formed in a 2-D array of Chua's circuits have been studied numerically. It has been found that spiral wave solutions can appear over a large range of parameters and some of their properties have been measured. This demonstrates that spiral wave dynamics can be studied in arrays of discrete electronic circuits, such as a 2-D array of Chua's circuits, where real-time results... View full abstract»

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  • A frequency approach for analyzing and controlling chaos in nonlinear circuits

    Publication Year: 1993 , Page(s): 819 - 828
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (768 KB)  

    The paper presents a frequency domain approach for studying the chaotic dynamics of an important class of nonlinear circuits. By formulating an elementary model of chaos and using the harmonic balance principle, techniques for the analysis and the stabilization to a periodic solution of complex systems are developed. They result in engineering tools which are simple and practical, although not rig... View full abstract»

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  • Piecewise-linear analysis of high-damping chaotic phase-locked loops using Melnikov's method

    Publication Year: 1993 , Page(s): 801 - 807
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (468 KB)  

    Studies the chaotic dynamics observed from a widely used second-order phase-locked loops (PLLs) operating as a frequency modulated demodulator. The authors apply Melnikov's method to high-damping PLLs to obtain the parameter range where there exist homoclinic points. This implies the PLL is chaotic in such a parameter range in view of the Smale-Birkhoff theorem. In particular, since the current PL... View full abstract»

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  • Strange attractors in delayed cellular neural networks

    Publication Year: 1993 , Page(s): 849 - 853
    Cited by:  Papers (41)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (296 KB)  

    A strange attractor has been found in a system described by a differential-difference equation: a delayed cellular neural network composed by only two cells. A detailed analysis of the set of eigenvalues that give rise to the attractor is presented and the bifurcation phenomena obtained by varying the delay are shown View full abstract»

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  • Chaotic dynamics of the driven Chua's circuit

    Publication Year: 1993 , Page(s): 836 - 840
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (372 KB)  

    The nonautonomous version of Chua's circuit exhibits a wide variety of bifurcation phenomena and chaotic structures depending upon the strength of the forcing parameters. In addition, control of chaos can be effected in this circuit. We also point out that synchronization of chaos is possible in this system, which can be effectively used for secure communication View full abstract»

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  • Confirmation of the Afraimovich-Shilnikov torus-breakdown theorem via a torus circuit

    Publication Year: 1993 , Page(s): 792 - 800
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (608 KB)  

    The Afraimovich-Shilnikov theorem on 2D torus breakdown is formulated and used to carry out a detailed numerical investigation of the bifurcation routes from the torus to chaos in a third-order torus circuit. Three scenarios of transition to chaos due to torus breakdown take place in this circuit in complete agreement with the theorem: 1) period-doubling bifurcations of the phase-locked limit cycl... View full abstract»

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  • Homoclinic and heteroclinic orbits of the three-cell cellular neural networks

    Publication Year: 1993 , Page(s): 843 - 848
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (376 KB)  

    A strange attractor has been found in a three-cell autonomous cellular neural network by simulation and experiment. It is shown in this paper that the theory of Shil'nikov can be applied for understanding the chaotic behaviors of this system View full abstract»

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