Stable Points, Stable Cycles and Chaos

1979 ◽  
pp. 59-75 ◽  
Author(s):  
James C. Frauenthal
Keyword(s):  
Stable Points

A discussion on orbital analysis - Longitude dependence of the geopotential, deduced from synchronous satellites

1967 ◽  
Vol 262 (1124) ◽  
pp. 137-143 ◽  
Keyword(s):  
Effective Potential ◽  
Dust Particles ◽  
Stable Plane ◽  
The Poor ◽  
Stable Points ◽  
Orbital Analysis

Observations of Syncom 2 and Syncom 3 during seven separate periods of free drift have been used in an attempt to find the effective potential at synchronous height. Although the accelerations are well determined near the two longitudes, 180° E and 300° E, where the observations are clustered, the poor distribution in longitude does not permit a satisfactory determination of individual coefficients. It would be particularly valuable to have observations in the region 0 to 40° E or around either of the two stable points near 70° E and 250° E. If there is or has been any significant population of dust particles in distant geocentric orbits, it is likely that a proportion will have been captured in the synchronous resonance, and will have accumulated near the stable positions. It is therefore suggested that it would be worth attempting to observe whether there are clouds of dust particles near the stable longitudes, and in the stable plane for synchronous height.

A Novel Memcapacitor and Its Application in a Chaotic Circuit

2021 ◽  
Author(s):  
Mei Guo ◽  
Ran Yang ◽  
Meng Zhang ◽  
Renyuan Liu ◽  
Yongliang Zhu ◽  
...  
Keyword(s):  
Steady State ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Burst Period ◽  
The Stability ◽  
Fifth Order ◽  
Stable Points

Abstract In this paper, a novel memcapacitor is designed by SBT memristor and two capacitors. A fifth-order memcapacitor and memristor chaotic circuit is proposed. The stability of the equilibrium point of the system is analyzed theoretically. Lyapunov exponents spectra, bifurcation diagrams, poincaré maps and phase diagrams are used to analyze the dynamic behaviors of the system. The results show that under different initial values and parameters, the system produces rich dynamic behaviors such as stable points, limit cycles, chaos, and so on. Specially, coexisting attractors, transient chaos, and steady-state chaos accompanied by burst period phenomenon are also produced in the system. The proposed memcapacitor-based circuit expands the research methods of memcapacitor for application in chaoticcircuits.

scholarly journals EQUILIBRIUM CONDITIONS IN BEACH WAVE INTERACTION

1972 ◽  
Vol 1 (13) ◽  
pp. 62 ◽  
Author(s):  
H. Raman
Keyword(s):  
Wave Interaction ◽  
Experimental Results ◽  
Laboratory Studies ◽  
Regular Waves ◽  
Equilibrium Conditions ◽  
Wave Characteristics ◽  
New Criterion ◽  
Constant Characteristics ◽  
Stable Points

Laboratory studies were conducted in an attempt to find out a relationship between beach and wave characteristics when equilibrium conditions are reached in beach wave interaction for the simple case of regular waves acting normal to the beach. Experimental results indicate the existence of stable points on beach profiles where the coordinates of the profile do not change with time when waves of constant characteristics act on the beach. Emperical relationship between the wave and beach properties are proposed. A new criterion for classification of beach profiles is indicated.

Semistable, Polystable and Stable Points (Part I)

2014 ◽  
pp. 131-139
Author(s):  
Gilberto Bini ◽  
Fabio Felici ◽  
Margarida Melo ◽  
Filippo Viviani
Keyword(s):  
Stable Points

Multiple Stable Points in Natural Communities

1974 ◽  
Vol 108 (964) ◽  
pp. 859-873 ◽  
Author(s):  
John P. Sutherland
Keyword(s):  
Stable Points ◽  
Natural Communities

scholarly journals Hamiltonian description of wave dynamics in nonequilibrium media

1994 ◽  
Vol 1 (4) ◽  
pp. 234-248 ◽  
Author(s):  
N. N. Romanova
Keyword(s):  
Nonlinear Wave ◽  
Evolution Equations ◽  
Normal Modes ◽  
Weak Nonlinearity ◽  
Hamiltonian Description ◽  
Weakly Nonlinear ◽  
Wave Dynamics ◽  
Canonical Variables ◽  
Stable Points ◽  
Stable Area

Abstract. We consider Hamiltonian description of weakly nonlinear wave dynamics in unstable and nonequilibrium media. We construct the appropriate canonical variables in the whole wavenumber space. The essentially new element is the construction of canonical variables in a vicinity of marginally stable points where two normal modes coalesce. The commonly used normal variables are not appropriate in this domain. The mater is that the approximation of weak nonlinearity breaks down when the dynamical system is written in terms of these variables. In this case we introduce the canonical variables based on the linear combination of modes belonging to the two different branches of dispersion curve. As an example of one of the possible applications of presented results the evolution equations for weakly nonlinear wave packets in the marginally stable area are derived. These equations cannot be derived if we deal with the commonly used normal variables.

CHAOS AND FRACTAL OF THE GENERAL TWO-DIMENSIONAL QUADRATIC MAP

2008 ◽  
Vol 22 (20) ◽  
pp. 3461-3471
Author(s):  
XINGYUAN WANG
Keyword(s):  
Fractal Dimension ◽  
General Feature ◽  
Strange Attractors ◽  
Two Dimensional ◽  
Control Parameters ◽  
Self Similarity ◽  
Boundary Equation ◽  
Quadratic Map ◽  
Fractal Images ◽  
Stable Points

The nature of the stable points of the general two-dimensional quadratic map is considered analytically, and the boundary equation of the first bifurcation of the map in the parameter space is given out. The general feature of the nonlinear dynamic activities of the map is analyzed by the method of numerical computation. By utilizing the Lyapunov exponent as a criterion, this paper constructs the strange attractors of the general two-dimensional quadratic map, and calculates the fractal dimension of the strange attractors according to the Lyapunov exponents. At the same time, the researches on the fractal images of the general two-dimensional quadratic map make it clear that when the control parameters are different, the fractal images are different from each other, and these fractal images exhibit the fractal property of self-similarity.

WALKING ON RATCHETS WITH TWO BROWNIAN MOTORS

2004 ◽  
Vol 04 (01) ◽  
pp. L161-L170 ◽  
Author(s):  
JOSE L. MATEOS
Keyword(s):  
Effective Diffusion ◽  
Diffusion Constant ◽  
Brownian Motors ◽  
Coherent Transport ◽  
Dimensionless Ratio ◽  
Bistable Potential ◽  
External Time ◽  
Stable Points ◽  
White Noises ◽  
Ratchet Potential

We analyze a model for a walker moving on an asymmetric periodic ratchet potential. This model is motivated by the properties of transport of the motor protein kinesin. The walker consists of two feet represented as two particles coupled nonlinearly through a double-well bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics where the ordering of the particles can alternate during the walking. The transitions between the two stable points on the bistable potential, correspond to a walking with alternating particles. In our model, each particle is acted upon by independent white noises, modeling thermal noise, and additionally we have an external time-dependent force that drives the system out of equilibrium, allowing directed transport. In the equilibrium case, where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns. In particular, we distinguish between two main walking styles: alternating and no alternating. These two ways of walking resemble the hand-over-hand and the inchworm walking in kinesin, respectively. Numerical simulations showed the existence of current reversals and significant changes in the effective diffusion constant. We obtained an optimal coherent transport, characterized by a maximum dimensionless ratio of the current and the effective diffusion (Péclet number), when the periodicity of the ratchet potential coincides with the equilibrium distance between the two particles.

Theory of viscoelastic behavior of regular polymeric networks with stable points linking four chains

1973 ◽  
Vol 6 (2) ◽  
pp. 190-195
Author(s):  
V. N. Pokrovskii ◽  
M. A. Chubisov
Keyword(s):  
Viscoelastic Behavior ◽  
Polymeric Networks ◽  
Stable Points
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