scholarly journals On a Simple Single-Transistor-Based Chaotic Snap Circuit: A Maximized Attractor Dimension at Minimized Damping and a Stable Equilibrium

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 116643-116660 ◽  
Author(s):  
Banlue Srisuchinwong ◽  
Buncha Munmuangsaen ◽  
Irfan Ahmad ◽  
Keerati Suibkitwanchai
Keyword(s):  
Stable Equilibrium ◽  
Attractor Dimension

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.

scholarly journals Nonlinear Compartment Models with Time-Dependent Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1657
Author(s):  
Jochen Merker ◽  
Benjamin Kunsch ◽  
Gregor Schuldt
Keyword(s):  
Stable Equilibrium ◽  
Compartment Model ◽  
Basins Of Attraction ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Compartment Models ◽  
Autonomous Case ◽  
Hyperbolic Equilibrium ◽  
Interior Points ◽  
Two Parameter

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

Temporal Dynamics of the Blueberry Maggot Fly (Diptera: Tephritidae) and its Primary Parasitoid, Biosteres melleus (Hymenoptera: Braconidae), in the Maine Wild Blueberry System

2019 ◽  
Vol 113 (2) ◽  
pp. 720-730 ◽  
Author(s):  
Francis A Drummond ◽  
Judith A Collins
Keyword(s):  
Predictive Model ◽  
Stable Equilibrium ◽  
Temporal Dynamics ◽  
Equilibrium Dynamics ◽  
Rhagoletis Mendax ◽  
Parasitism Rates ◽  
Blueberry Maggot Fly ◽  
Rates Of Growth ◽  
Wild Blueberry ◽  
Insecticide Sprays

Abstract Between 1998 and 2017, we conducted studies in wild blueberry, Vaccinium angustifolium Aiton (Ericales: Ericaceae), to elucidate the temporal dynamics of the blueberry maggot fly, Rhagoletis mendax Curran, and its parasitoid, Biosteres melleus (Gahan). A predictive model for the emergence of R. mendax was validated at two sites over 3 yr. A second predictive model for the major parasitoid, B. melleus, of R. mendax was constructed and suggests that the delay in emergence of the parasitoid relative to its host provides a period or ‘biological window’ of 9 d where insecticide sprays can be applied to manage R. mendax with a limited impact on the parasitoid. A 20-yr study on the parasitoid/host dynamics showed parasitism rates ranging from 0.5 to 28.2%. It appears that R. mendax populations in Maine wild blueberry are characterized by stable equilibrium dynamics, significantly affected by stochastic processes. There was a weak, but significant relationship between B. melleus density and R. mendax intrinsic rates of growth. Our data suggest that R. mendax population dynamics in wild blueberry is characterized by an unstable equilibrium tipping point of 7.9 maggots per liter of blueberries or an average of 10 flies per trap.

Achieving Multistability Through Use of a Single Bistable Compliant Mechanism

2010 ◽  
Author(s):  
Guimin Chen ◽  
Yanjie Gou ◽  
Aimei Zhang
Keyword(s):  
Stable Equilibrium ◽  
Compliant Mechanism ◽  
Power Input ◽  
Successful Operation ◽  
New Approaches ◽  
Reconfigurable Robots ◽  
Bistable Mechanism

A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.

scholarly journals Stability and Hopf Bifurcation Analysis of Coupled Optoelectronic Feedback Loops

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Gang Zhu ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Normal Form ◽  
Center Manifold ◽  
Stable Equilibrium ◽  
Feedback Loops ◽  
Asymptotically Stable ◽  
Center Manifold Theorem ◽  
Feedback Strength ◽  
Coupling Parameters ◽  
Normal Form Method

The dynamics of a coupled optoelectronic feedback loops are investigated. Depending on the coupling parameters and the feedback strength, the system exhibits synchronized asymptotically stable equilibrium and Hopf bifurcation. Employing the center manifold theorem and normal form method introduced by Hassard et al. (1981), we give an algorithm for determining the Hopf bifurcation properties.

scholarly journals Metastable and stable equilibrium states of stellar electron-nuclear plasmas

2005 ◽  
Vol 336 (4-5) ◽  
pp. 370-377 ◽  
Author(s):  
F. Ferro ◽  
A. Lavagno ◽  
P. Quarati
Keyword(s):  
Stable Equilibrium ◽  
Equilibrium States

On the Existence of Multiple Equilibrium States in Strained-Layer Superlattices

1987 ◽  
Vol 103 ◽  
Author(s):  
William C. Johnson
Keyword(s):  
Free Energy ◽  
Equilibrium State ◽  
Stable Equilibrium ◽  
Multiple Equilibrium ◽  
Equilibrium Thermodynamic ◽  
Relative Thickness ◽  
Two Phase ◽  
Strained Layer ◽  
Strained Layer Superlattice ◽  
Strained Layer Superlattices

ABSTRACTUsing recent results from the thermodynamics of stressed solids, two-phase coexistence in a simple binary strained-layer superlattice is examined. We show that for a given temperature and overall composition of the superlattice, there can exist more than one linearly stable, equilibrium thermodynamic state. That is, there may exist several combinations of relative thickness of the phases and corresponding phase compositions that minimize the free energy of the system. The equilibrium state observed experimentally can, therefore, be influenced by the processing path.

scholarly journals The genetic variability of polygenic characters under optimizing selection, mutation and drift

1972 ◽  
Vol 19 (1) ◽  
pp. 17-25 ◽  
Author(s):  
M. G. Bulmer
Keyword(s):  
Genetic Variability ◽  
Stable Equilibrium ◽  
Finite Size ◽  
Approximate Expression ◽  
Average Amount

SUMMARYThe effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci with equal effects without dominance was investigated theoretically. Conditions for a stable equilibrium under selection and mutation, in the absence of drift, have been obtained, and hence the amount of genetic variability which can be maintained by mutation has been determined. An approximate expression for the average amount of genetic variability to be expected in the presence of drift in a population of finite size has also been obtained and evaluated.

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