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# IEEE Transactions on Circuits and Systems

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Displaying Results 1 - 16 of 16
• ### Complicated dynamics of prototype continuous-line adaptive control system

Publication Year: 1988, Page(s):842 - 849
Cited by:  Papers (22)  |  Patents (1)
| | PDF (600 KB)

The authors investigate the possible dynamics that a prototype model reference adaptive control system can experience when using the so-called σ-modification adaption law described by P.I. Ioannou and P.V. Kokotovic (1984). Limiting their attention to first-order plants with a single unknown pole and an external disturbance, they verify analytically the bifurcations that an example adaptive ... View full abstract»

• ### Bifurcation effects in robust adaptive control

Publication Year: 1988, Page(s):835 - 841
Cited by:  Papers (24)
| | PDF (560 KB)

A specific adaptive control problem is analyzed in a search for the implication of undermodeling on the performance of adaptive control. The observed bifurcation phenomena (Hopf bifurcation, homoclinic points, etc.) indicate what kind of dynamical responses are possible in the adaptive system. Because these phenomena are structurally stable with respect to small (non)linear disturbances and singul... View full abstract»

• ### Reality of chaos in the double scroll circuit: A computer-assisted proof

Publication Year: 1988, Page(s):909 - 925
Cited by:  Papers (38)
| | PDF (1308 KB)

The authors prove three key inequalities stated in the paper by L.O. Chua, M. Komouro, and T. Matsumoto (see ibid., vol. CAS-33, p. 1072-1118, 1986) by giving verifiable error bounds to the quantities involved in the inequalities with an assistance of a computer. This provides another rigorous proof that the so-called double scroll circuit is chaotic in the sense of Shilnikov. Since a computer is ... View full abstract»

• ### An analysis of truncated fractal growths in the stability boundaries of three-node swing equations

Publication Year: 1988, Page(s):825 - 834
Cited by:  Papers (22)
| | PDF (764 KB)

A second-order nonautonomous ordinary differential equation (the transiently forced pendulum system), is studied and the existence of fractally intertwined stability domains is reported for certain ranges of parameters in the time-dependent forcing function. The analysis is extended to a modified version of Sitnikov's three-body problem in celestial mechanics. Parallels are drawn with the three-bo... View full abstract»

• ### Chaos in a four-variable piecewise-linear system of differential equations

Publication Year: 1988, Page(s):902 - 908
Cited by:  Papers (16)
| | PDF (388 KB)

A set of four piecewise-linear ordinary differential equations in four variables is examined. The system has a single positive Lyapunov characteristic exponent. Over a parameter range, however, the Kaplan-Yorke dimension is greater than three, and the Poincare section appears to have two continuous directions. An example is discussed in which the equations describe a chemical system whose solution... View full abstract»

• ### Degenerate Hopf bifurcations in power systems

Publication Year: 1988, Page(s):818 - 824
Cited by:  Papers (19)
| | PDF (1304 KB)

The occurrence of degenerate Hopf bifurcations in power systems is considered and this phenomenon is explored analytically using the Lyapunov-Schmidt reduction method and by simulation. A qualitative method that uses system trajectory data to classify the type of degenerate Hopf bifurcation is proposed View full abstract»

• ### Normal forms for constrained nonlinear differential equations. I. Theory

Publication Year: 1988, Page(s):881 - 901
Cited by:  Papers (16)
| | PDF (1244 KB)

The theory of normal forms for smooth vector fields is system nonlinear differential-algebraic equations. Such equations are widely encountered in practical circuits and systems when parasitics play an important role in the system's qualitative behavior. Such parasitics are a called small parameters in the associated singular perturbation problem. The approach taken from here is completely differe... View full abstract»

• ### The dynamics of coupled current-biased Josephson junctions

Publication Year: 1988, Page(s):810 - 817
Cited by:  Papers (17)
| | PDF (572 KB)

Some numerical and analytical results are presented that illustrate how changes in the coupling strength affect the dynamics of coupled current-biased Josephson point junctions are presented. It is shown that in certain cases there is a unique interval during which the basic running solution for the equations governing the dynamics of the couples system is unstable. The numerical results suggest t... View full abstract»

• ### Normal forms for nonlinear vector fields. I. Theory and algorithm

Publication Year: 1988, Page(s):863 - 880
Cited by:  Papers (47)
| | PDF (1160 KB)

Normal forms are analytical tools for studying the qualitative behavior of the nonlinear vector fields. A tutorial for the nonspecialist in general, and the circuit theorist in particular, on the basic concept and foundation of the modern theory of normal forms for nonlinear vector fields, is presented. After stating the Poincare and the Takens normal form, the latest refinements due to S. Ushiki ... View full abstract»

• ### Spatio-temporal complexity in nonlinear image processing

Publication Year: 1988, Page(s):770 - 780
Cited by:  Papers (15)
| | PDF (872 KB)

A pictorial survey is presented of pattern dynamics in video feedback and in related numerical methods. After introduction to video feedback apparatus and concepts from dynamical systems theory, a range of phenomena are presented, from simple attractor types to homogeneous video turbulence. Examples of complex behavior include symmetry-locking chaos, spatial amplification of fluctuations in open f... View full abstract»

• ### Quasi-periodicity and dynamical systems: An experimentalist's view

Publication Year: 1988, Page(s):790 - 809
Cited by:  Papers (107)
| | PDF (1896 KB)

Current theoretical and experimental work on quasiperiodicity is reviewed in this tutorial. The concept of universality and its relevance to experiments on nonlinear multifrequency systems is discussed. The reduction of experimental data using Poincare sections and the mathematical properties of the one-dimensional circle map are considered. Various dynamical systems technique for determining scal... View full abstract»

• ### Normal forms near critical points for differential equations and maps

Publication Year: 1988, Page(s):850 - 862
Cited by:  Papers (20)
| | PDF (796 KB)

The normal-form theory is a technique of transforming an original vector field to a simpler form by an appropriate change of coordinates, so that the essential features of the flow become more evident. A basic theory of normal forms, based on the classical idea of Poincare and Birkhoff, is presented. Normal forms for vector fields and diffeomorphisms are discussed, and their relationship is consid... View full abstract»

• ### Strange attractors that govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential

Publication Year: 1988, Page(s):781 - 783
Cited by:  Papers (14)
| | PDF (28 KB)

Four examples are shown which demonstrate the use of computer graphics to visualize chaotic attractors from EEGs (electroencephalograms). The recordings are made from multiple sites: factor analysis is used to partition the variance into orthogonal components, and the largest three serve best to represent the dynamics in the three Euclidean dimensions accessible using a flight simulator. It is the... View full abstract»

• ### Flare': A graphic by-product of the study of a two-dimensional dynamical system

Publication Year: 1988, Page(s):768 - 769
| | PDF (244 KB)

A piece of mathematical art' titled Flare' is presented. Flare was obtained as a by-product of the study of the iteration of a certain (unnamed) function of two variables. This study is related to the Mandlebrot set but it does not concern the quadratic map zz2+c. Some general comments are presented on the background of such representations and use of ... View full abstract»

• ### Stable vortex rings of excitation in neuroelectric media

Publication Year: 1988, Page(s):784 - 787
Cited by:  Papers (9)
| | PDF (252 KB)

The membranes of living cells, for example, in heart muscle, support electric dipoles which invert momentarily following an electrical stimulus that exceeds a threshold. The pulse propagates as an action potential' at about 0.5 mm/ms in the three-dimensional foam' of cellular membranes. Four computer generated panels are shown which graphically represent such waves, using a continuum model with ... View full abstract»

• ### Phoenix

Publication Year: 1988, Page(s):788 - 789
| | PDF (140 KB)

A picture is presented called the Phoenix, which represents a complex-one-dimensional section of a Julia-like' set of a complexified `Henon map.' The Phoenix appears when the attractive fixed point of the mapping f(x,y=(x2+c =by, x) where c and b are the complex constants, loses its stability via a saddle-... View full abstract»