Some chaotic properties of 2-𝒟 rational discrete map

FROM FANCY TO FACT

PEDIATRICS ◽

10.1542/peds.50.5.685 ◽

1972 ◽

Vol 50 (5) ◽

pp. 685-687

Author(s):

Robert E. Greenberg

Keyword(s):

Human Physiology ◽

Laboratory Finding ◽

Effective Therapy ◽

Cellular Mechanisms ◽

Main Route ◽

Abnormal Laboratory ◽

Abnormal Laboratory Finding ◽

Discrete Map

Recognition of a given symptom, sign, or abnormal laboratory finding represents the start of a long, often tortuous path. The trail soon broadens, as combinations of findings coalesce into syndromes. Blind alleys, thick forests, and divergent roads beguile and confuse the traveler. One may stumble onto the main route by application of rational, physiologic patterns of thought. Charting a discrete map to finite understanding and effective therapy is dependent upon delineation of underlying cellular mechanisms. Similar parables have often been utilized to indicate the applicability and essentiality of studies of cellular and intercellular processes in relation to human physiology and disease.

Download Full-text

LOCAL ACTIVITY CRITERIA FOR DISCRETE-MAP CNN

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402005157 ◽

2002 ◽

Vol 12 (06) ◽

pp. 1227-1272 ◽

Cited By ~ 8

Author(s):

VALERY I. SBITNEV ◽

LEON O. CHUA

Keyword(s):

Logistic Map ◽

Period Doubling ◽

Spiral Wave ◽

Vortex Pinning ◽

Magnetic Vortex ◽

Critical Threshold ◽

Local Activity ◽

Cell Impedance ◽

Initial Setting ◽

Discrete Map

Discrete-time CNN systems are studied in this paper by the application of Chua's local activity principle. These systems are locally active everywhere except for one isolated parameter value. As a result, nonhomogeneous spatiotemporal patterns may be induced by any initial setting of the CNN system when the strength of the system diffusion coupling exceeds a critical threshold. The critical coupling coefficient can be derived from the loaded cell impedance of the CNN system. Three well-known 1D map CNN's (namely, the logistic map CNN, the magnetic vortex pinning map CNN, and the spiral wave reproducing map CNN) are introduced to illustrate the applications of the local activity principle. In addition, we use the cell impedance to demonstrate the period-doubling scenario in the logistic and the magnetic vortex pinning maps.

Download Full-text

Quasi-Periodicity, Chaos and Coexistence in the Time Delay Controlled Two-Cell DC–DC Buck Converter

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414501247 ◽

2014 ◽

Vol 24 (10) ◽

pp. 1450124 ◽

Cited By ~ 4

Author(s):

Karama Koubaâ ◽

Moez Feki

Keyword(s):

Numerical Simulation ◽

Time Delay ◽

Chaotic Attractor ◽

Chaotic Behavior ◽

Buck Converter ◽

Design Parameters ◽

Bifurcation And Chaos ◽

Different Types ◽

2D Torus ◽

Discrete Map

In addition to border collision bifurcation, the time delay controlled two-cell DC/DC buck converter is shown to exhibit a chaotic behavior as well. The time delay controller adds new design parameters to the system and therefore the variation of a parameter may lead to different types of bifurcation. In this work, we present a thorough analysis of different scenarios leading to bifurcation and chaos. We show that the time delay controlled two-cell DC/DC buck converter may also exhibit a Neimark–Sacker bifurcation which for some parameter set may lead to a 2D torus that may then break yielding a chaotic behavior. Besides, the saturation of the controller can also lead to the coexistence of a stable focus and a chaotic attractor. The results are presented using numerical simulation of a discrete map of the two-cell DC/DC buck converter obtained by expressing successive crossings of Poincaré section in terms of each other.

Download Full-text