Why metabolic systems are rarely chaotic

Scheper, Tjeerd Olde

doi:10.1016/j.biosystems.2008.05.020

Cited by 5 publications

(11 citation statements)

References 17 publications

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“…Attempts to control different chaotic systems have been successful, but it appears that some terms in a set of equations are more effective at controlling the chaotic dynamics than others. This is more obvious in a relatively simple system, such as the Ikeda map [11], but in more complex dynamic systems this is not readily evident. A systematic analysis of the relative contributions of rate control of different system variables may be required to determine if this effect is due to the control method, or due to properties of the chaotic system itself.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the addition of an extra feedback controller in the standard Lorenz model [18], creates a system that can demonstrate periodic orbits, chaos and hyper-chaos (with more than one positive Lyapunov exponent). This system is described by equations (12) to (15), with the control function (11). The inclusion of RCC can stabilise this system even more readily than the three dimensional Lorenz system, due to the presence of the feedback loop (see figure 5), which is why only one control function is sufficient.…”

Section: Rcc Of Lorenz Systemsmentioning

confidence: 99%

“…For different RCC parameters (shown is ξ = −0.5, µ = 3), different oscillation patterns can be achieved. Although RCC can modify the underlying stable oscillation (as is the case with the Lorenz system), the qualitative dynamic behaviour of the system has not changed and allows the RCC to be enabled even when the system is already stable (see also [11]). The equations (24) to (27) describe the controlled Belousov-Zhabotinsky system, and (23) is the appropriate RCC function.…”

Section: B Belousov-zhabotinsky Reactionmentioning

confidence: 99%

“…Previously, a method of chaotic control, that was derived from the concept of metabolic control, has been proposed [11]. The Rate Control of Chaos (RCC) method has demonstrated the principle of control of complex unstable dynamics, based on feedforward localised control.…”

Section: Introductionmentioning

confidence: 99%

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Biologically inspired rate control of chaos

Scheper

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

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Section: Discussionmentioning

confidence: 99%

Section: Rcc Of Lorenz Systemsmentioning

confidence: 99%

Section: B Belousov-zhabotinsky Reactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Biologically inspired rate control of chaos

Scheper

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The complex chemical chaotic system has the ability to self-regulate through a simple feedback loop. Some work has denoted that feedback interactions could impart precision, robustness and versatility to intercellular signals during animal development [16].…”

Section: Chaotic Dynamics Of the Minimal Willamowski-rössler Systemmentioning

confidence: 99%

Chaos control for Willamowski–Rössler model of chemical reactions

Bodale

Oancea²

2015

Chaos, Solitons & Fractals

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Harmonic Versus Chaos Controlled Oscillators in Hexapedal Locomotion

Fuente

Lones

Crook

et al. 2015

Information Processing in Cells and Tissues

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The behavioural diversity of chaotic oscillator can be controlled into periodic dynamics and used to model locomotion using central pattern generators. This paper shows how controlled chaotic oscillators may improve the adaptation of the robot locomotion behaviour to terrain uncertainties when compared to nonlinear harmonic oscillators. This is quantitatively assesses by the stability, changes of direction and steadiness of the robotic movements. Our results show that the controlled Wu oscillator promotes the emergence of adaptive locomotion when deterministic sensory feedback is used. They also suggest that the chaotic nature of chaos controlled oscillators increases the expressiveness of pattern generators to explore new locomotion gaits.

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Why metabolic systems are rarely chaotic

Cited by 5 publications

References 17 publications

Biologically inspired rate control of chaos

Biologically inspired rate control of chaos

Chaos control for Willamowski–Rössler model of chemical reactions

Harmonic Versus Chaos Controlled Oscillators in Hexapedal Locomotion

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