Local Attractors for Gradient-related Descent Iterations

2012 ◽  
Keyword(s):  
Local Attractors

ESS modelling of diploid populations II: stability analysis of possible equilibria

1994 ◽  
Vol 26 (2) ◽  
pp. 361-376 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Stability Analysis ◽  
Evolutionarily Stable Strategy ◽  
Companion Paper ◽  
Stable Strategy ◽  
Local Attractors ◽  
The Mean ◽  
Arbitrary Frequency ◽  
Probability Simplex ◽  
Evolutionarily Stable ◽  
Diploid Populations

In order to determine the robustness of the mean-covariance approach to exploring behavioural models of sexual diploid biological populations which are based on the evolutionarily stable strategy (ESS) concept, a companion paper explored relevant features of the probability simplex of allelic frequencies for a population which is genetically homogeneous except possibly at a single locus.The Shahshahani metric is modified in this paper to produce a measure of distance near an arbitrary frequency F in the allelic simplex which can be used when some alleles are given zero weight by F. The equation of evolution for the modified metric can then be used to show that certain sets of frequencies (corresponding to equilibrium mean strategies) act as local attractors, as long as the mean strategies corresponding to those sets are non-singular or even, in most cases, singular. We identify conditions under which the measure of distance from an initial frequency to a nearby set of equilibrium frequencies corresponding to exceptional mean strategies might increase, either temporarily or for a protracted length of time.

COMPLEX DYNAMICS IN COUPLED NONLINEAR ELEMENT SYSTEMS

1991 ◽  
Vol 05 (08) ◽  
pp. 1179-1214 ◽  
Author(s):  
KENJU OTSUKA
Keyword(s):  
Nonlinear Oscillator ◽  
Complex Dynamics ◽  
Landau Equation ◽  
Computer Experiments ◽  
Time Dependent ◽  
Chain Model ◽  
Ginzburg Landau ◽  
Physical Systems ◽  
Local Attractors ◽  
Discrete Complex

This paper reviews complex dynamics which arise through the interaction of simple nonlinear elements without chaotic response, including self-induced switching among local attractors (chaotic itinerancy) and related phenomena. Several realistic physical systems consisting of coupled nonlinear elements are considered on the basis of computer experiments: coupled nonlinear oscillator (e.g., discrete complex time-dependent Ginzburg-Landau equation) systems, coupled laser arrays, and a coupled multistable optical chain model.

Tuning in to Slow Events

2019 ◽  
pp. 135-157
Author(s):  
Mari Riess Jones
Keyword(s):  
Global Attractor ◽  
Mode Locking ◽  
Neural Oscillations ◽  
Transient Mode ◽  
Time Patterns ◽  
Traditional Mode ◽  
Local Attractors

This chapter addresses entrainments in various slow events. It challenges the idea that only slow events that are isochronous are capable of entraining neural oscillations. It tackles entrainments in events that afford quasi-isochronous driving rhythms as well as in events that are markedly non-isochronous (but coherent). Coherent sequences have time patterns as in short-short-long or long-short-short sequences. This is an important chapter as it differentiates two entrainment protocols: traditional mode-locking versus transient mode-locking. Traditional mode-locking is familiar; it describes entrainment when neither the driving rhythm nor the driven rhythm change significantly (fluctuations are all right). Traditional mode-locking is governed by a single (global) attractor. By contrast, transient mode-locking refers to fleeting entrainments to changing driving rhythms, given the persisting period of driven oscillation. This form of mode-locking delivers a series of (local) attractors. This chapter develops these ideas and provides many examples.

Local attractors for weakly damped forced KdV equation in thin 2D domains

2000 ◽  
Vol 21 (10) ◽  
pp. 1131-1138 ◽  
Author(s):  
Tian Li-xin ◽  
Liu Yu-rong ◽  
Liu Zeng-rong
Keyword(s):  
Kdv Equation ◽  
Local Attractors
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