THE FEASIBLE DOMAINS AND THEIR BIFURCATIONS IN AN EXTENDED LOGISTIC MODEL WITH AN EXTERNAL INTERFERENCE

2007 ◽  
Vol 17 (03) ◽  
pp. 877-889 ◽  
Author(s):  
EN-GUO GU
Keyword(s):  
Discrete Model ◽  
Logistic Model ◽  
Focal Point ◽  
Basins Of Attraction ◽  
Two Dimensional ◽  
External Interference ◽  
Feasible Set ◽  
Coexistence Of Attractors

This paper is devoted to the study of the properties of basins of attraction and the domains of feasible trajectories (discrete trajectories having an ecological sense) generated by a family of two-dimensional map T related to a discrete model of populations generation. The inverse of T has vanishing denominator giving rise to nonclassical singularities: a nondefinition line, a focal point and a prefocal line. Furthermore, the differences and relations between the feasible set, the feasible domains and the basins of attraction are presented. A phenomena of coexistence of attractors is shown. The structure of a chaotic repellor is interpreted by use of the singularities.

KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 545-555 ◽  
Author(s):  
F. TRAMONTANA ◽  
L. GARDINI ◽  
D. FOURNIER-PRUNARET ◽  
P. CHARGE
Keyword(s):  
Focal Point ◽  
Singular Line ◽  
Two Dimensional ◽  
Focal Points ◽  
Singular Set ◽  
One Dimensional ◽  
Attracting Set ◽  
Straight Line ◽  
Special Character ◽  
Stable And Unstable Sets

We consider the class of two-dimensional maps of the plane for which there exists a whole one-dimensional singular set (for example, a straight line) that is mapped into one point, called a "knot point" of the map. The special character of this kind of point has been already observed in maps of this class with at least one of the inverses having a vanishing denominator. In that framework, a knot is the so-called focal point of the inverse map (it is the same point). In this paper, we show that knots may also exist in other families of maps, not related to an inverse having values going to infinity. Some particular properties related to focal points persist, such as the existence of a "point to slope" correspondence between the points of the singular line and the slopes in the knot, lobes issuing from the knot point and loops in infinitely many points of an attracting set or in invariant stable and unstable sets.

ON TWO-DIMENSIONAL DYNAMICAL SYSTEMS ASSOCIATED WITH MEMBRANE KINETICS UNDERLYING CARDIAC ARRHYTHMIAS

2009 ◽  
Vol 19 (05) ◽  
pp. 1709-1732 ◽  
Author(s):  
B. M. BAKER ◽  
M. E. KIDWELL ◽  
R. P. KLINE ◽  
I. POPOVICI
Keyword(s):  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Two Dimensional ◽  
Stimulus Period ◽  
Smooth Maps ◽  
Periodic Stimulation ◽  
Piecewise Smooth Maps ◽  
Dimensional Version ◽  
Bifurcation Law ◽  
The One

We study the orbits, stability and coexistence of orbits in the two-dimensional dynamical system introduced by Kline and Baker to model cardiac rhythmic response to periodic stimulation — as a function of (a) kinetic parameters (two amplitudes, two rate constants) and (b) stimulus period. The original paper focused mostly on the one-dimensional version of this model (one amplitude, one rate constant), whose orbits, stability properties, and bifurcations were analyzed via the theory of skew-tent (hence unimodal) maps; the principal family of orbits were so-called "n-escalators", with n a positive integer. The two-dimensional analog (motivated by experimental results) has led to the current study of continuous, piecewise smooth maps of a polygonal planar region into itself, whose dynamical behavior includes the coexistence of stable orbits. Our principal results show (1) how the amplitude parameters control which escalators can come into existence, (2) escalator bifurcation behavior as the stimulus period is lowered — leading to a "1/n bifurcation law", and (3) the existence of basins of attraction via the coexistence of three orbits (two of them stable, one unstable) at the first (largest stimulus period) bifurcation. We consider the latter result our most important, as it is conjectured to be connected with arrhythmia.

Two-dimensional motion of a rolling non-circular cylinder on a flat horizontal surface

2018 ◽  
Vol 96 (6) ◽  
pp. 627-632
Author(s):  
Amir Aghamohammadi ◽  
Mohammad Khorrami
Keyword(s):  
Circular Cylinder ◽  
Energy Conservation ◽  
Cross Section ◽  
Equilibrium Configuration ◽  
Focal Point ◽  
Center Of Mass ◽  
Horizontal Surface ◽  
Two Dimensional ◽  
Small Oscillations ◽  
Equilibrium Configurations

The two dimensional motion of a generally non-circular non-uniform cylinder on a flat horizontal surface is investigated. Assuming that the cylinder does not slip, energy conservation is used to study the motion in general. Points of returns, and small oscillations around equilibrium configuration are studied. As examples, cylinders are studied for which the cross section is an ellipse, with the center of mass at the center of the ellipse or at a focal point, and the frequencies of small oscillations around their equilibrium configurations are found. The conditions for losing contact or sliding are also investigated. Finally, the motion is studied in more detail for the case of a nearly circular cylinder.

A passive dynamic walking model with Coulomb friction at the hip joint

Robotica ◽  
2013 ◽  
Vol 31 (8) ◽  
pp. 1221-1227 ◽  
Author(s):  
Wenhao Guo ◽  
Tianshu Wang ◽  
Qi Wang
Keyword(s):  
Hip Joint ◽  
Coulomb Friction ◽  
Basins Of Attraction ◽  
Swing Phase ◽  
Dynamic Equations ◽  
Two Dimensional ◽  
Dynamic Walking ◽  
Passive Dynamic Walking ◽  
Impact Phase ◽  
The Impact

SUMMARYThis paper presents a modified passive dynamic walking model with hip friction. We add Coulomb friction to the hip joint of a two-dimensional straight-legged passive dynamic walker. The walking map is divided into two parts – the swing phase and the impact phase. Coulomb friction and impact make the model's dynamic equations nonlinear and non-smooth, and a numerical algorithm is given to deal with this model. We study the effects of hip friction on gait and obtain basins of attraction of different coefficients of friction.

scholarly journals Two-Dimensional Discrete Model for Buckling of Helical Springs

2019 ◽  
Vol 24 ◽  
pp. 28-39 ◽  
Author(s):  
Francesco De Crescenzo ◽  
Pietro Salvini
Keyword(s):  
Discrete Model ◽  
Two Dimensional ◽  
Helical Springs

scholarly journals SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

Dynamics of a Piecewise-Linear Oscillator With Limited Power Supply

2009 ◽  
Author(s):  
Silvio L. T. de Souza ◽  
Ibereˆ L. Caldas ◽  
Jose´ M. Balthazar ◽  
Reyolando M. L. R. F. Brasil
Keyword(s):  
Power Supply ◽  
Piecewise Linear ◽  
Basins Of Attraction ◽  
Point Of View ◽  
Restoring Force ◽  
Rich Variety ◽  
Coexistence Of Attractors ◽  
Limited Power ◽  
Limited Power Supply ◽  
Basins Of Attractions

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction.

Quasisoliton states in a two-dimensional discrete model

1995 ◽  
Vol 52 (21) ◽  
pp. 15273-15278 ◽  
Author(s):  
A. La Magna ◽  
R. Pucci ◽  
G. Piccitto ◽  
F. Siringo
Keyword(s):  
Discrete Model ◽  
Two Dimensional

scholarly journals On Some Properties of Focal Points

2009 ◽  
Vol 2009 ◽  
pp. 1-11
Author(s):  
M. R. Ferchichi ◽  
I. Djellit
Keyword(s):  
Fixed Point ◽  
Focal Point ◽  
Two Dimensional ◽  
Focal Points ◽  
Dynamical Properties

We consider some dynamical properties of two-dimensional maps having an inverse with vanishing denominator. We put in evidence a link between a fixed point of a map with fractional inverse and a focal point of this inverse.

Simulation of a 2D Channel Flow Around a Square Obstacle with Lattice-Boltzmann (BGK) Automata

1998 ◽  
Vol 09 (08) ◽  
pp. 1129-1141 ◽  
Author(s):  
J. Bernsdorf ◽  
Th. Zeiser ◽  
G. Brenner ◽  
F. Durst
Keyword(s):  
Flow Field ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Focal Point ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Blockage Ratio ◽  
Two Dimensional ◽  
Viscous Incompressible Flows ◽  
Turbulent Flow Field

Results for time-dependent, viscous, incompressible flows were investigated using the lattice-Boltzmann (BGK) automata. The decay of a synthetic turbulent flow field and the time evolution of an initial vortex were simulated for validation purposes. The focal point was the investigation of the instationary flow around a square obstacle in a two-dimensional channel for a range of Reynolds numbers between 80 and 300 and a blockage ratio of 0.125. The Strouhal number was measured for this case and found to be in the range of data given in the literature.

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