Iris center location using Hough transform with two-dimensional parameter space

2012 ◽  
Vol 51 (6) ◽  
pp. 785-791 ◽  
Author(s):  
I. A. Matveev
Keyword(s):  
Parameter Space ◽  
Hough Transform ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Center Location ◽  
Iris Center

COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

2007 ◽  
Vol 17 (09) ◽  
pp. 3071-3083 ◽  
Author(s):  
J. M. GONZÀLEZ-MIRANDA
Keyword(s):  
Phase Diagram ◽  
Bifurcation Diagram ◽  
Parameter Space ◽  
Neuron Model ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Rapid Responses ◽  
Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Parameter Space ◽  
Landau Theory ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Theory Analysis ◽  
Continuous Transition ◽  
Dimensional Parameter ◽  
First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

Effects of DC electric fields on neuronal excitability: A bifurcation analysis

2014 ◽  
Vol 28 (18) ◽  
pp. 1450114 ◽  
Author(s):  
Yanqiu Che ◽  
Huiyan Li ◽  
Chunxiao Han ◽  
Xile Wei ◽  
Bin Deng ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Parameter Space ◽  
Bifurcation Analysis ◽  
Neural Control ◽  
Neuronal Excitability ◽  
Modulation Method ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Dc Electric Fields

In this paper, the effects of external DC electric fields on the neuro-computational properties are investigated in the context of Morris–Lecar (ML) model with bifurcation analysis. We obtain the detailed bifurcation diagram in two-dimensional parameter space of externally applied DC current and trans-membrane potential induced by external DC electric field. The bifurcation sets partition the two-dimensional parameter space in terms of the qualitatively different behaviors of the ML model. Thus the neuron's information encodes the stimulus information, and vice versa, which is significant in neural control. Furthermore, we identify the electric field as a key parameter to control the transitions among four different excitability and spiking properties, which facilitates the design of electric fields based neuronal modulation method.

DIFFERENT BIFURCATION SCENARIOS OF NEURAL FIRING PATTERNS OBSERVED IN THE BIOLOGICAL EXPERIMENT ON IDENTICAL PACEMAKERS

2013 ◽  
Vol 23 (12) ◽  
pp. 1350195 ◽  
Author(s):  
HUAGUANG GU
Keyword(s):  
Parameter Space ◽  
Period Doubling ◽  
Two Dimensional ◽  
Neural Firing ◽  
Biological Experiment ◽  
Dimensional Parameter ◽  
Simple Process ◽  
Firing Patterns ◽  
Complex Process ◽  
Different Levels

Two different bifurcation scenarios of spontaneous neural firing patterns with decreasing extracellular calcium concentrations were observed in the biological experiment on identical pacemakers when potassium concentrations were fixed at two different levels. Six typical experimental scenarios manifesting dynamics closely matching those previously simulated using the Hindmarsh–Rose model and Chay model are provided as representative examples. Bifurcation scenarios from period-1 bursting to period-1 spiking via a complex process and via a simple process, period-doubling bifurcation to chaos, period-adding bifurcation with chaos, and period-adding bifurcation with stochastic burstings were identified. The results not only reveal that an experimental neural pacemaker is capable of generating different bifurcation scenarios but also provide a basic framework for bifurcations in neural firing patterns in a two-dimensional parameter space.

Quasiperiodicity and Chaos in a Generalized Nosé–Hoover Oscillator

2016 ◽  
Vol 26 (10) ◽  
pp. 1650170 ◽  
Author(s):  
Paulo C. Rech
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Parameter Space ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
First Order ◽  
Chaotic Region ◽  
Quasiperiodic Structures

This paper reports on an investigation of the two-dimensional parameter-space of a generalized Nosé–Hoover oscillator. It is a mathematical model of a thermostated harmonic oscillator, which consists of a set of three autonomous first-order nonlinear ordinary differential equations. By using Lyapunov exponents to numerically characterize the dynamics of the model at each point of this parameter-space, it is shown that dissipative quasiperiodic structures are present, embedded in a chaotic region. The same parameter-space is also used to confirm the multistability phenomenon in the investigated mathematical model.

Exact duality of the dissipative Hofstadter model on a triangular lattice: T-duality and noncommutative algebra

2016 ◽  
Vol 31 (27) ◽  
pp. 1650154
Author(s):  
Taejin Lee
Keyword(s):  
Parameter Space ◽  
Triangular Lattice ◽  
Uniform Magnetic Field ◽  
Quantum Wires ◽  
Temperature Limit ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Dimensional Parameter ◽  
Noncommutative Algebra ◽  
Dual Transformation

We study the dissipative Hofstadter model on a triangular lattice, making use of the [Formula: see text] T-dual transformation of string theory. The [Formula: see text] dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.

Imaginary Scators Bound Set Under the Iterated Quadratic Mapping in 1 + 2 Dimensional Parameter Space

2016 ◽  
Vol 26 (01) ◽  
pp. 1630002 ◽  
Author(s):  
M. Fernández-Guasti
Keyword(s):  
Parameter Space ◽  
Complex Structure ◽  
Three Dimensional ◽  
Periodic Points ◽  
Mandelbrot Set ◽  
Three Dimensions ◽  
Quadratic Mapping ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Nilpotent Elements

The quadratic iteration is mapped within a nondistributive imaginary scator algebra in [Formula: see text] dimensions. The Mandelbrot set is identically reproduced at two perpendicular planes where only the scalar and one of the hypercomplex scator director components are present. However, the bound three-dimensional S set projections change dramatically even for very small departures from zero of the second hypercomplex plane. The S set exhibits a rich fractal-like boundary in three dimensions. Periodic points with period [Formula: see text], are shown to be necessarily surrounded by points that produce a divergent magnitude after [Formula: see text] iterations. The scator set comprises square nilpotent elements that ineluctably belong to the bound set. Points that are square nilpotent on the [Formula: see text]th iteration, have preperiod 1 and period [Formula: see text]. Two-dimensional plots are presented to show some of the main features of the set. A three-dimensional rendering reveals the highly complex structure of its boundary.

The bandcount increment scenario. II. Interior structures

2008 ◽  
Vol 464 (2097) ◽  
pp. 2247-2263 ◽  
Author(s):  
Viktor Avrutin ◽  
Bernd Eckstein ◽  
Michael Schanz
Keyword(s):  
Canonical Form ◽  
Parameter Space ◽  
Complex Interaction ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
One Dimensional ◽  
Self Similar ◽  
Bifurcation Structures

Bifurcation structures in the two-dimensional parameter spaces formed by chaotic attractors alone are still far away from being understood completely. In a series of three papers, we investigate the chaotic domain without periodic inclusions for a map, which is considered by many authors as some kind of one-dimensional canonical form for discontinuous maps. In this second part, we investigate fine substructures nested into the basic structures reported and explained in part I. It is demonstrated that the overall structure of the chaotic domain is caused by a complex interaction of bandcount increment, bandcount adding and bandcount doubling structures, whereby some of them are nested into each other ad infinitum leading to self-similar structures in the parameter space.

A Geometrical Approach Assessing Instability Trends for Galloping

1991 ◽  
Vol 58 (3) ◽  
pp. 784-791 ◽  
Author(s):  
P. Yu ◽  
N. Popplewell ◽  
A. H. Shah
Keyword(s):  
Wind Speed ◽  
Parameter Space ◽  
Degrees Of Freedom ◽  
Critical Conditions ◽  
Geometrical Approach ◽  
Two Dimensional ◽  
Electrical Conductor ◽  
Geometrical Method ◽  
Dimensional Parameter ◽  
The Stability

Although the galloping of an iced electrical conductor has been considered by many researchers, no special attention has been given to the galloping’s sensitivity to alternations in the system’s parameters. A geometrical method is presented in this paper to describe these instability trends and to provide compromises for controlling an instability. The conventional but uncontrollable parameter of the wind speed is chosen as the basis for obtaining the critical conditions under which bifurcations occur for a representative two degrees-of-freedom model. Variations in these critical conditions are found in a two-dimensional parameter space in order to determine the trends for the initiation of galloping as well as to evaluate the stability of the ensuring periodic vibrations.

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