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Properties of Isostables and Basins of Attraction of Monotone Systems
[article]
2016
arXiv
pre-print
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In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. ...
We discuss computational approaches to estimate isostables and basins of attraction and illustrate the results on two and four state monotone systems. ...
CONCLUSION In this paper, we study geometric properties of monotone systems such as properties of isostables and basins of attraction. ...
arXiv:1510.01153v2
fatcat:zd6nvcvuxrhnjiiaeerjlcuh6m
Geometric Properties of Isostables and Basins of Attraction of Monotone Systems
[article]
2017
arXiv
pre-print
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In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator theory. ...
We also show how variations in basins of attraction can be bounded under parametric uncertainty in the vector field of monotone systems. ...
Geometric Properties of Isostables and Basins of Attraction of Monotone Systems Aivar Sootla and Alexandre Mauroy Abstract-In this paper, we study geometric properties of basins of attraction of monotone ...
arXiv:1705.02853v1
fatcat:vfgxfalkcfcdrniv7oxpafuxay
Optimal control formulation of pulse-based control using Koopman operator
2018
Automatica
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It was recently shown that, for monotone bistable systems, this problem admits easy-to-implement open-loop solutions in terms of temporal pulses (i.e., step functions of fixed length and fixed magnitude ...
We show that this problem can be solved using a static optimization problem in the case of monotone systems. ...
Assume now that the system is monotone with two exponentially stable equilibria x * and x • and basins of attraction B(x * ) and B(x • ), respectively. ...
doi:10.1016/j.automatica.2018.01.036
fatcat:36avoe4ixfcyzlsrteypdcvmka
Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty
2018
IEEE Transactions on Automatic Control
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Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems. ...
In applications, such as biomedicine and systems/synthetic biology, technical limitations in actuation complicate implementation of time-varying control signals. ...
We finally mention spectral properties of monotone systems ( [13] ). ...
doi:10.1109/tac.2017.2736941
fatcat:vmeamib4rnbo5ddgsj7ionn6v4
Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty
[article]
2017
arXiv
pre-print
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Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems. ...
In applications, such as biomedicine and systems/synthetic biology, technical limitations in actuation complicate implementation of time-varying control signals. ...
We finally mention spectral properties of monotone systems ( [13] ). ...
arXiv:1708.00232v1
fatcat:rt4nxltibbdzjg4tudbbppdgim
Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator
2016
IFAC-PapersOnLine
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The original framework was derived for monotone systems and all the extensions relied on monotone systems theory. ...
Additionally, we show that for monotone systems the switching function is also monotone in some sense, a property that can yield efficient algorithms to compute it. ...
Assumptions A1 and A2 guarantee the existence of eigenfunctions s * 1 (x) and s • 1 (x) that are continuously differentiable on each basin of attraction. ...
doi:10.1016/j.ifacol.2016.10.247
fatcat:6sfocc62v5ddfofpiwqnfbrxpa
Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator
[article]
2016
arXiv
pre-print
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The original framework was derived for monotone systems and all the extensions relied on monotone systems theory. ...
Additionally, we show that for monotone systems the switching function is also monotone in some sense, a property that can yield efficient algorithms to compute it. ...
Assumptions A1 and A2 guarantee the existence of eigenfunctions s * 1 (x) and s • 1 (x) that are continuously differentiable on each basin of attraction. ...
arXiv:1605.06252v1
fatcat:inhipqirfrgz3fj7kuaoyjmbqq
Operator-Theoretic Characterization of Eventually Monotone Systems
[article]
2017
arXiv
pre-print
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In order to provide a characterization, we drew inspiration from the results for linear systems, where eventually monotone (positive) systems are studied using the spectral properties of the system (i.e ...
Perron-Frobenius property). ...
We conclude this subsection by a corollary of Theorem 1, which describes the geometric properties of the system in the basin of attraction. ...
arXiv:1510.01149v3
fatcat:jr6wriw7sbftliffy24m7f2xrm
Global computation of phase-amplitude reduction for limit-cycle dynamics
2018
Chaos
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basin of attraction of the limit cycle. ...
We illustrate the method by computing the so-called isostables of limit cycles in two, three, and four-dimensional state spaces, as well as their responses to strong external inputs. ...
We note that, in the case of planar systems, this is an exact (non-reduced) representation of the system in the basin of attraction of the limit cycle.
C. ...
doi:10.1063/1.5030175
pmid:30070491
fatcat:mqfchfnoibfgxnrizvppqodody
An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum
[article]
2016
arXiv
pre-print
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A connection is drawn between these two interpretations of a dynamical system by means of establishing a link between the spectral properties of the Koopman operator and the geometric properties in the ...
We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. ...
Basin of attraction The basin of a specific limit cycle p 1 can be found by repeatedly computing the pre-images of the map (13) . ...
arXiv:1608.08734v1
fatcat:a6nommyskbeztcledufejdg2bu
An operator-theoretic approach to differential positivity
2015
2015 54th IEEE Conference on Decision and Control (CDC)
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In this paper, we investigate the general connections between the (geometric) properties of differentially positive systems and the (spectral) properties of the Koopman operator. ...
In particular, we obtain converse results for differential positivity, showing for instance that any hyperbolic limit cycle is differentially positive in its basin of attraction. ...
is strictly differentially positive in the basin of attraction B(Γ) ⊆ R n of Γ. ...
doi:10.1109/cdc.2015.7403327
dblp:conf/cdc/MauroyFS15
fatcat:7pvofe6jpjgu5edv5xmheemveu
An operator-theoretic approach to differential positivity
[article]
2015
arXiv
pre-print
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In this paper, we investigate the general connections between the (geometric) properties of differentially positive systems and the (spectral) properties of the Koopman operator. ...
In particular, we obtain converse results for differential positivity, showing for instance that any hyperbolic limit cycle is differentially positive in its basin of attraction. ...
is strictly differentially positive in the basin of attraction B(Γ) ⊆ R n of Γ. ...
arXiv:1504.01548v1
fatcat:yngajdzecjdbhfndzziancnuj4
Effects of pH on Proteins: Predictions for Ensemble and Single-Molecule Pulling Experiments
2011
Journal of the American Chemical Society
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We provide a framework based on the Molecular Transfer Model (MTM) to account for pH effects on the properties of globular proteins. ...
The phase diagrams of CI2 and protein G as a function of f and pH are dramatically different and reflect the underlying pH-dependent stability changes in the absence of force. ...
This work was supported in part by grants from the National Science Foundation (NSF; 09-14033) and National Institutes of Health (NIH; GM089685) to D.T. and an NIH Graduate Partnerships Program (GPP) Biophysics ...
doi:10.1021/ja206557y
pmid:22148729
pmcid:PMC3262061
fatcat:xno5r56wqvcnde7bundzwv7v2y
A geometric approach to Phase Response Curves and its numerical computation through the parameterization method
[article]
2018
arXiv
pre-print
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Moreover, we link the existence properties of this invariant curve as the amplitude of the perturbation is increased with changes in the PRC waveform and with the geometry of isochrons. ...
The underlying idea relies on the construction of a periodic system whose corresponding stroboscopic map has an invariant curve. ...
We also acknowledge the use of the UPC Dynamical Systems group's cluster for research computing (https://dynamicalsystems.upc.edu/en/computing/). ...
arXiv:1809.07318v1
fatcat:xh236iot2nb2po4opyufdrw5fe
Sequencing of folding events in Go-type proteins
2000
Journal of Chemical Physics
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2000 pre-print arXiv:cond-mat/0008201v1 fatcat:wk7oqn4fqjg2zlyrbhkjvknkwa
The folding scenarios for CI2 and SH3 are consistent with experimental studies of their transition states. ...
The order of events depends primarily on the geometry of the native state. Variations in temperature, coupling strengths and viscosity affect the sequencing scenarios to a rather small extent. ...
In Section 3, we discuss ways to delineate the native basin and we determine the folding properties of the models. The mechanisms of folding for each of the proteins are discussed in Section 4. ...
doi:10.1063/1.1314868
fatcat:e334k6vpovgq7phb3gi2ae4i3u
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