Coordination of side-to-side head movements and walking in amphetamine-treated rats: a stereotyped motor pattern as a stable equilibrium in a dynamical system

1996 ◽  
Vol 74 (6) ◽  
pp. 487-495 ◽  
Author(s):  
Neri Kafkafi ◽  
Stavit Levi-Havusha ◽  
Ilan Golani ◽  
Yoav Benjamini
Keyword(s):  
Dynamical System ◽  
Stable Equilibrium ◽  
Motor Pattern ◽  
Head Movements

ON ASYMPTOTICALLY STABILIZING THE RABINOVICH DYNAMICAL SYSTEM

2012 ◽  
Vol 09 (05) ◽  
pp. 1220008 ◽  
Author(s):  
RAMONA A. TUDORAN
Keyword(s):  
Dynamical System ◽  
Stable Equilibrium ◽  
Equilibrium States

In this paper we give a method to stabilize asymptotically the nontrivial Lyapunov stable equilibrium states of the Rabinovich dynamical system.

scholarly journals Durophagy in sharks: feeding mechanics of the hammerhead Sphyrna tiburo

2000 ◽  
Vol 203 (18) ◽  
pp. 2781-2796 ◽  
Author(s):  
C.D. Wilga ◽  
P.J. Motta
Keyword(s):  
Motor Activity ◽  
High Speed ◽  
Motor Pattern ◽  
Adductor Muscle ◽  
Head Movements ◽  
Motor Patterns ◽  
Apparent Lack ◽  
Sphyrna Tiburo ◽  
Adductor Muscles ◽  
Feeding Mechanics

This study investigates the motor pattern and head movements during feeding of a durophagus shark, the bonnethead Sphyrna tiburo, using electromyography and simultaneous high-speed video. Sphyrna tiburo feeds almost exclusively on hard-shelled crabs, with shrimp and fish taken occasionally. It captures crabs by ram feeding, then processes or reduces the prey by crushing it between molariform teeth, finally transporting the prey by suction for swallowing. The prey-crushing mechanism is distinct from that of ram or bite capture and suction transport. This crushing mechanism is accomplished by altering the duration of jaw adductor muscle activity and modifying jaw kinematics by the addition of a second jaw-closing phase. In crushing events, motor activity of the jaw adductor muscles continues (biting of the prey occurs as the jaws close and continues after the jaws have closed) throughout a second jaw-closing phase, unlike capture and transport events during which motor activity (biting) ceases at jaw closure. Sphyrna tiburo is able to take advantage of a resource (hard prey) that is not readily available to most sharks by utilizing a suite of durophagous characteristics: molariform teeth, a modified jaw protrusor muscle, altered jaw adductor activity and modified jaw kinematics. Sphyrna tiburo is a specialist feeder on crab prey as demonstrated by the lack of differences in kinematic or motor patterns when offered prey of differing hardness and its apparent lack of ability to modulate its behavior when feeding on other prey. Functional patterns are altered and coupled with modifications in dental and jaw morphology to produce diverse crushing behaviors in elasmobranchs.

METASTABILITY FOR RANDOM PERTURBATIONS OF NEARLY-HAMILTONIAN SYSTEMS

2008 ◽  
Vol 08 (01) ◽  
pp. 1-21 ◽  
Author(s):  
AVANTI ATHREYA ◽  
MARK FREIDLIN
Keyword(s):  
Dynamical System ◽  
Stable Equilibrium ◽  
Random Perturbation ◽  
Equilibrium Points ◽  
Stochastic Perturbation ◽  
Averaging Principle ◽  
Random Perturbations ◽  
Small Random Perturbation ◽  
Finite Set ◽  
Single State

We characterize the phenomenon of metastability for a small random perturbation of a nearly-Hamiltonian dynamical system. We use the averaging principle and the theory of large deviations to prove that the metastable "state" is, in general, not a single state but rather a nondegenerate probability measure across the stable equilibrium points of the unperturbed Hamiltonian system. The set of all possible "metastable distributions" is a finite set that is independent of the stochastic perturbation.

scholarly journals Freely forming groups: Trying to be rare

2006 ◽  
Vol 48 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Michael Baake ◽  
Uwe Grimm ◽  
Harald Jockusch
Keyword(s):  
Dynamical System ◽  
Finite Number ◽  
Continuous Time ◽  
Stable Equilibrium ◽  
Logistic Equation ◽  
Infinite Population ◽  
Dependent Model ◽  
Frequency Dependent Model ◽  
Globally Stable ◽  
Smooth Dynamical System

AbstractA simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical system that reaches its globally stable equilibrium in finite time. This dynamical system is sufficiently simple to permit an explicit solution, built piecewise from solutions of the logistic equation in continuous time. It displays an interesting tree-like structure of coalescing components.

COEXISTENCE OF POINT, PERIODIC AND STRANGE ATTRACTORS

2013 ◽  
Vol 23 (05) ◽  
pp. 1350093 ◽  
Author(s):  
JULIEN CLINTON SPROTT ◽  
XIONG WANG ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Strange Attractor ◽  
Chaotic Attractor ◽  
Stable Equilibrium ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
New Chaotic System ◽  
Point Attractor ◽  
New System

For a dynamical system described by a set of autonomous ordinary differential equations, an attractor can be a point, a periodic cycle, or even a strange attractor. Recently, a new chaotic system with only one stable equilibrium was described, which locally converges to the stable equilibrium but is globally chaotic. This paper further shows that for certain parameters, besides the point attractor and chaotic attractor, this system also has a coexisting stable limit cycle, demonstrating that this new system is truly complicated and interesting.

Bursting Oscillations and the Mechanism with Sliding Bifurcations in a Filippov Dynamical System

2018 ◽  
Vol 28 (12) ◽  
pp. 1850146 ◽  
Author(s):  
Rui Qu ◽  
Yu Wang ◽  
Guoqing Wu ◽  
Zhengdi Zhang ◽  
Qinsheng Bi
Keyword(s):  
Dynamical System ◽  
Natural Frequency ◽  
Stable Equilibrium ◽  
Multiple Scales ◽  
Hopf Bifurcations ◽  
Periodic Excitation ◽  
Nonsmooth Boundary ◽  
Bursting Oscillations ◽  
First Case ◽  
Exciting Frequency

The main purpose of the paper is to investigate the effect of multiple scales in frequency domain on the complicated oscillations of Filippov system with discontinuous right-hand side. A relatively simple model based on the Chua’s circuit with periodic excitation is introduced as an example. When the exciting frequency is far less than the natural frequency, implying that an order gap between the exciting frequency and the natural frequency exists, the whole exciting term can be considered as a slow-varying parameter, based on which the bifurcations of the two subsystems in different regions divided by the nonsmooth boundary are presented. Two typical cases are considered, which correspond to different distributions of equilibrium branches as well as the related bifurcations. In the first case, periodic symmetric Hopf/Hopf-fold-sliding bursting oscillations can be obtained, in which Hopf bifurcations may cause the alternations between the quiescent states and the spiking states, while fold bifurcations connect the two quiescent states moving along the stable equilibrium branches and sliding along the nonsmooth boundary, respectively. While the second case is the periodic symmetric fold/fold-fold-sliding bursting, where the fold bifurcations not only lead to the alternations between the quiescent states and the spiking states, but also connect the two quiescent states moving along the stable equilibrium branches and sliding along the nonsmooth boundary, respectively. It is pointed out that, different from the bursting oscillations in smooth dynamical systems in which the bifurcations may cause the alternations between quiescent states and spiking states, in the nonsmooth system, bifurcations may not only lead to the alternations, but also connect different forms of quiescent states. Furthermore, in the Filippov system, sliding movement along the nonsmooth boundary can be observed, the mechanism of which is presented based on the analysis of the two subsystems in different regions.

Microtwinning Evidence For The Apparent Five-Fold Symmetry in T2(Al6Li3Cu)

1987 ◽  
Vol 45 ◽  
pp. 24-25
Author(s):  
Kenneth S. Vecchio ◽  
David B. Williams
Keyword(s):  
Stable Equilibrium ◽  
Equilibrium Phase ◽  
Convergent Beam Electron Diffraction ◽  
Icosahedral Structure ◽  
Cubic Crystals ◽  
Icosahedral Phases ◽  
Heat Treated ◽  
Zero Layer ◽  
Convergent Beam ◽  
Zr Alloy

Since the discovery in 1984 by Shechtman et al. of crystals which display apparent five-fold symmetry, extensive effort has been given to establishing a theoretical basis for the existence of icosahedral phases (eg.2.). Several other investigations have been centered on explaining these observations based on twinning of cubic crystals (eg.3.). Recently, the existence of a stable, equilibrium phase T2Al6 Li3Cu) possessing an icosahedral structure has been reported in the Al-Li-Cu system(4-6).In the present study an Al-2.6wt.%Li-l.5wt.%Cu-0.lwt.%Zr alloy was heat treated at 300°C for 100hrs. to produce large T2 precipitates. Convergent Beam Electron Diffraction (CBED) patterns were obtained from two-fold, three-fold, and apparent five-fold axes of T2 particles. Figure 1 shows the five-fold symmetric zero layer CBED pattern obtained from T2 particles.

Role of pinnae and head movements in localizing pure tones 1The authors would like to thank Mr. Remi Humbert for implementing the experiment in Turbo Pascal and for his further assistance.

1999 ◽  
Vol 58 (3) ◽  
pp. 170-179 ◽  
Author(s):  
Barbara S. Muller ◽  
Pierre Bovet
Keyword(s):  
Sound Source ◽  
Head Movement ◽  
Movement Analysis ◽  
Head Movements ◽  
Sound Sources ◽  
Localization Accuracy ◽  
Sound Effects ◽  
Posterior Quadrant ◽  
Localization Performance ◽  
Pure Tones

Twelve blindfolded subjects localized two different pure tones, randomly played by eight sound sources in the horizontal plane. Either subjects could get information supplied by their pinnae (external ear) and their head movements or not. We found that pinnae, as well as head movements, had a marked influence on auditory localization performance with this type of sound. Effects of pinnae and head movements seemed to be additive; the absence of one or the other factor provoked the same loss of localization accuracy and even much the same error pattern. Head movement analysis showed that subjects turn their face towards the emitting sound source, except for sources exactly in the front or exactly in the rear, which are identified by turning the head to both sides. The head movement amplitude increased smoothly as the sound source moved from the anterior to the posterior quadrant.

Sign in / Sign up

Export Citation Format

Share Document