A theory for adaptation and competition applied to logistic map dynamics

Pierre, Darren E.; Hübler, Alfred

doi:10.1016/0167-2789(94)90292-5

Cited by 13 publications

(9 citation statements)

References 8 publications

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“…x n (a) ≈ δ n if a leads to chaotic x dynamics 0 if a leads to periodic x dynamics (5) where δ n is a nonzero number. Equation 5 can be understood in terms of the recurrence time and power spectrum of the x n dynamics of the logistic map.…”

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confidence: 99%

Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map

et al. 2000

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Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.

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confidence: 99%

Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map

et al. 2000

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“…Synchronization of two coupled escapement-driven pendulum clocks is already investigated [42]. Blekhman [43] discusses observations of the Dutch researcher Christian Huygens 9 and presents the results of a laboratory reproduction and a theoretical analysis of oscillators coupled through 9 Christian Huygens is probably the first scientist who observed and described the synchronization phenomenon. a common supporting frame.…”

Section: Synchronizationmentioning

confidence: 99%

“…8. Edge of chaos has been found to be the optimal setting for control of a system [9]. A selfadjusting system is a system in which the control of a parameter value depends on previous states of the system [10].…”

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confidence: 99%

Dynamics of oscillators coupled by a medium with adaptive impact

Daneshvar

2013

Complexity

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In this article, we study the dynamics of coupled oscillators. We use mechanical metronomes that are placed over a rigid base. The base moves by a motor in a one-dimensional direction and the movements of the base follow some functions of the phases of the metronomes (in other words, it is controlled to move according to a provided function). Because of the motor and the feedback, the phases of the metronomes affect the movements of the base, whereas on the other hand, when the base moves, it affects the phases of the metronomes in return. For a simple function for the base movement (such as y = γ x [rθ 1 + (1 − r)θ 2 ] in which y is the velocity of the base, γ x is a multiplier, r is a proportion, and θ 1 and θ 2 are phases of the metronomes), we show the effects on the dynamics of the oscillators. Then, we study how this function changes in time when its parameters adapt by a feedback. By numerical simulations and experimental tests, we show that the dynamic of the set of oscillators and the base tends to evolve towards a certain region. This region is close to a transition in dynamics of the oscillators, where more frequencies start to appear in the frequency spectra of the phases of the metronomes. We interpret this as an adaptation towards the edge of chaos.

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“…Co-evolution to the edge of chaos is discussed in [50]. Edge of chaos has been found to be the optimal setting for control of a system [51]. A self-adjusting system is a system in which the control of a parameter value depends on previous states of the system [52].…”

Section: E Self-adjusting Systems and The Edge Of Chaosmentioning

confidence: 99%

Synchronization of Mechanical Oscillators: An Experimental Study

Daneshvar

́r-Nagy

2011

Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts a and B

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In this paper we investigate synchronization of oscillators. We use mechanical metronomes that are coupled through a mechanical medium. In passive coupling of two oscillators, the coupling medium is a one degree of freedom passive mechanical basis. The analysis of the system is shown and supported by simulations of the proposed model and experimental results. We show how the oscillators synchronize and discuss the affecting parameters in synchronization. In another case, the oscillators are forced by an external input while that input is also affected by the oscillators. This feedback loop introduces dynamics to the whole system. For this case, we place the mechanical metronomes on a one degree of freedom moving base. The movements of the base are a function of a feedback from the phases of the metronomes. We study the space of possibilities for the movements of the base and consider impacts of the base movement on the synchronization of metronomes. We also show how such a system evolves in time when we introduce an adjusting parameter that changes over time and updates based on feedbacks from the system.

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A theory for adaptation and competition applied to logistic map dynamics

Cited by 13 publications

References 8 publications

Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map

Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map

Dynamics of oscillators coupled by a medium with adaptive impact

Synchronization of Mechanical Oscillators: An Experimental Study

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