Patterns of Human Interlimb Coordination Emerge from the Properties of Non-Linear, Limit Cycle Oscillatory Processes

1981 ◽  
Vol 13 (4) ◽  
pp. 226-261 ◽  
Author(s):  
J. A. Scott Kelso ◽  
Kenneth G. Holt ◽  
Philip Rubin ◽  
Peter N. Kugler
Keyword(s):  
Limit Cycle ◽  
Interlimb Coordination ◽  
Linear Limit ◽  
Non Linear ◽  
Oscillatory Processes

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

Some limit theorems for a supercritical branching process allowing immigration

1976 ◽  
Vol 13 (1) ◽  
pp. 17-26 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Population Growth ◽  
Limit Theorems ◽  
Branching Process ◽  
Random Variable ◽  
Positive Random Variable ◽  
Linear Limit ◽  
Non Linear ◽  
The Mean

We consider the Bienaymé–Galton–Watson model of population growth in which immigration is allowed. When the mean number of offspring per individual, α, satisfies 1 < α < ∞, a well-known result proves that a normalised version of the size of the n th generation converges to a finite, positive random variable iff a certain condition is satisfied by the immigration distribution. In this paper we obtain some non-linear limit theorems when this condition is not satisfied. Results are also given for the explosive case, α = ∞.

Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non-linear energy sinks

2006 ◽  
Vol 13 (1) ◽  
pp. 41-75 ◽  
Author(s):  
Young S. Lee ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman ◽  
D. Michael McFarland
Keyword(s):  
Limit Cycle ◽  
Van Der Pol Oscillator ◽  
Limit Cycle Oscillations ◽  
Van Der Pol ◽  
Non Linear

scholarly journals Extending Complex Conjugate Control to Nonlinear Wave Energy Converters

2020 ◽  
Vol 8 (2) ◽  
pp. 84
Author(s):  
David G. Wilson ◽  
Rush D. Robinett ◽  
Giorgio Bacelli ◽  
Ossama Abdelkhalik ◽  
Ryan G. Coe
Keyword(s):  
Energy Harvesting ◽  
Limit Cycle ◽  
Wave Energy ◽  
Limit Cycles ◽  
Reactive Power ◽  
Complex Conjugate ◽  
Linear Wave ◽  
Wave Energy Converters ◽  
Linear Limit ◽  
Energy Converters

This paper extends the concept of Complex Conjugate Control (CCC) of linear wave energy converters (WECs) to nonlinear WECs by designing optimal limit cycles with Hamiltonian Surface Shaping and Power Flow Control (HSSPFC). It will be shown that CCC for a regular wave is equivalent to a power factor of one in electrical power networks, equivalent to mechanical resonance in a mass-spring-damper (MSD) system, and equivalent to a linear limit cycle constrained to a Hamiltonian surface defined in HSSPFC. Specifically, the optimal linear limit cycle is defined as a second-order center in the phase plane projection of the constant energy orbit across the Hamiltonian surface. This concept of CCC described by a linear limit cycle constrained to a Hamiltonian surface will be extended to nonlinear limit cycles constrained to a Hamiltonian surface for maximum energy harvesting by the nonlinear WEC. The case studies presented confirm increased energy harvesting which utilizes nonlinear geometry realization for reactive power generation.

Nonlinear Climate Dynamics: from Deterministic Behavior to Stochastic Excitability and Chaos

2020 ◽  
Author(s):  
Michel Crucifix ◽  
Dmitri Alexandrov ◽  
irina Bashkirtseva ◽  
Lev Ryashko
Keyword(s):  
Limit Cycle ◽  
Large Scale ◽  
Ice Age ◽  
Orbital Forcing ◽  
Stochastic Forcing ◽  
Present Contribution ◽  
Non Linear ◽  
Stochastic Sensitivity Analysis ◽  
Deterministic Behavior ◽  
Earth Dynamics

&lt;p&gt;Glacial-interglacial cycles are global climatic changes which have characterised the last 3 million years. The eight latest&lt;br&gt;glacial-interglacial cycles represent changes in sea level over 100 m, and their average duration was around 100 000 years. There is a&lt;br&gt;long tradition of modelling glacial-interglacial cycles with low-order dynamical systems. In one view, the cyclic phenomenon is caused by&lt;br&gt;non-linear interactions between components of the climate system: The dynamical system model which represents Earth dynamics has a limit cycle. In an another view, the variations in ice volume and ice sheet extent are caused by changes in Earth's orbit, possibly amplified by feedbacks.&lt;br&gt;This response and internal feedbacks need to be non-linear to explain the asymmetric character of glacial-interglacial cycles and their duration. A third view sees glacial-interglacial cycles as a limit cycle synchronised on the orbital forcing.&lt;/p&gt;&lt;p&gt;The purpose of the present contribution is to pay specific attention to the effects of stochastic forcing. Indeed, the trajectories&lt;br&gt;obtained in presence of noise are not necessarily noised-up versions of the deterministic trajectories. They may follow pathways which&lt;br&gt;have no analogue in the deterministic version of the model. &amp;#160;Our purpose is to&lt;br&gt;demonstrate the mechanisms by which stochastic excitation may generate such large-scale oscillations and induce intermittency. To this end, we&lt;br&gt;consider a series of models previously introduced in the literature, starting by autonomous models with two variables, and then three&lt;br&gt;variables. The properties of stochastic trajectories are understood by reference to the bifurcation diagram, the vector field, and a&lt;br&gt;method called stochastic sensitivity analysis. &amp;#160;We then introduce models accounting for the orbital forcing, and distinguish forced and&lt;br&gt;synchronised ice-age scenarios, and show again how noise may generate trajectories which have no immediate analogue in the determinstic model.&amp;#160;&lt;/p&gt;

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