Comparison between constant feedback and limiter controllers

Zhou, C. T.; Yu, M. Y.

doi:10.1103/physreve.71.016204

Cited by 7 publications

(1 citation statement)

References 37 publications

(71 reference statements)

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“…For example, maps with a horizontal part occur frequently in power electronics as models for DC-DC converters Saito et al 2007). Maps of this kind have also been proposed as a simple method for controlling cardiac chaos (Glass & Zeng 1994) or, in general, controlling chaotic behaviour using the simple limiter control method (Corron et al 2000;Murali & Sinha 2003;Stoop & Wagner 2003;Zhou & Yu 2005). They occur also as local maps in coupled map lattices used in biological and economic models (Sinha 1994).…”

Section: Introductionmentioning

confidence: 99%

On a bifurcation structure mimicking period adding

2011

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In this work, we investigate a piecewise-linear discontinuous scalar map defined on three partitions. This map is specifically constructed in such a way that it shows a recently discovered bifurcation scenario in its pure form. Owing to its structure on the one hand and the similarities to the nested period-adding scenario on the other hand, we denoted the new bifurcation scenario as nested period-incrementing bifurcation scenario. The new bifurcation scenario occurs in several physical and electronical systems but usually not isolated, which makes the description complicated. By isolating the scenario and using a suitable symbolic description for the asymptotically stable periodic orbits, we derive a set of rules in the space of symbolic sequences that explain the structure of the stable periodic domain in the parameter space entirely. Hence, the presented work is a necessary step for the understanding of the more complicated bifurcation scenarios mentioned above.

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Section: Introductionmentioning

confidence: 99%

On a bifurcation structure mimicking period adding

2011

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Threshold harvesting as a conservation or exploitation strategy in population management

Hilker

Liz

2020

Theor Ecol

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Threshold harvesting removes the surplus of a population above a set threshold and takes no harvest below the threshold. This harvesting strategy is known to prevent overexploitation while obtaining higher yields than other harvesting strategies. However, the harvest taken can vary over time, including seasons of no harvest at all. While this is undesirable in fisheries or other exploitation activities, it can be an attractive feature of management strategies where removal interventions are costly and desirable only occasionally. In the presence of population fluctuations, the issue of variable harvests and population sizes becomes even more notorious. Here, we investigate the impact of threshold harvesting on the dynamics of both population size and harvests, especially in the presence of population cycles. We take into account semelparous and iteroparous life cycles, Allee effects, observation uncertainty, and demographic as well as environmental stochasticity, using generic mathematical models in discrete time. Our results show that threshold harvesting enhances multiple forms of population stability, namely persistence, constancy, resilience, and dynamic stability. We discuss plausible choices of threshold values, depending on whether the aim is resource exploitation, pest control, or the stabilization of fluctuations.

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Stabilizing long-period orbits via symbolic dynamics in simple limiter controllers

Zhou

2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We present an efficient approach to determine the control parameter of simple limiter controllers by using symbolic dynamics of one-dimensional unimodal maps. By applying addition- and subtraction-symbol rules for generating an admissible periodic sequence, we deal with the smallest base problem of the digital tent map. The proposed solution is useful for minimizing the configuration of digital circuit designs for a given target sequence. With the use of the limiter controller, we show that one-dimensional unimodal maps may be robustly employed to generate the maximum-length shift-register sequences. For an arbitrary long Sarkovskii sequence, the control parameters are analytically given.

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Comparison between constant feedback and limiter controllers

Cited by 7 publications

References 37 publications

On a bifurcation structure mimicking period adding

On a bifurcation structure mimicking period adding

Threshold harvesting as a conservation or exploitation strategy in population management

Stabilizing long-period orbits via symbolic dynamics in simple limiter controllers

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