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1 ematic drift toward a set of stable states ("attractors").
2 ral chaos but gives rise to a "double spiral attractor".
3 small number of important industrial metals (attractors).
4 and the groups of nodes that determine each attractor.
5 of preceding destabilization of a progenitor attractor.
6 sory cues (i.e. the landmarks) onto the ring attractor.
7 regulatory genes induced a jump to a nearby attractor.
8 of teaching is to make the content taught an attractor.
9 xample, autoencoders store the example as an attractor.
10 ctions are greatly eased from that of a line attractor.
11 imulus information is not a fixed-point type attractor.
12 with tumor grade, and a lymphocyte-specific attractor.
13 lls both as a plane attractor and as a point attractor.
14 uit with dynamics resembling those of a ring attractor.
15 ctivity arises from a low-dimensional spiral attractor.
16 point, instead of being obligatory resource attractors.
17 ttern separation and memory storage via bump attractors.
18 characterize the detailed structure of cell attractors.
19 onnective evolution end in non-modular local attractors.
20 urating neurons and their convergence toward attractors.
21 ions, which we show are composed of discrete attractors.
22 esponse curves, tipping points and alternate attractors.
23 most probable transition paths between those attractors.
24 ction is limited by the demand for the major attractors.
25 works (GRNs) at the boundary between dynamic attractors.
26 duced switch between high-dimensional cancer attractors.
27 in computes using low-dimensional continuous attractors.
28 n the presence of latent "ghost" multistable attractors.
29 n of two networks that have adopted distinct attractors.
30 by recurrent network structures called ring attractors.
31 y master regulators and destabilizers of its attractors.
32 of a hybrid system model and identifying all attractors.
33 failed to correlate with either the NE or ML attractors.
34 ed set of variables that control the size of attractors (a proxy for resilience), such as population
35 ecies may be drawn towards a single midpoint attractor - a unimodal gradient of environmental favoura
36 ion D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate o
38 n transitions between a silent and an active attractor and assumed that neurons fired Poisson spike t
39 altered the transition rate into the silent attractor and reproduced the relation between correlatio
40 ition of each year in relation to the fitted attractors and assumed tipping points of the fold bifurc
43 dynamical systems theory and the concepts of attractors and repellors, we develop an understanding of
44 be understood by finding stable steady-state attractors and the most probable transition paths betwee
45 rized autoencoders store training samples as attractors and thus iterating the learned map leads to s
47 These stable patterns function as 'dynamic attractors' and provide a feature that is characteristic
48 d as a ring attractor, grid cells as a plane attractor, and place cells both as a plane attractor and
50 ttractor, the fixed-point strange nonchaotic attractor, and the critical behavior with the maximum Ly
51 non-additive modelling to estimate alternate attractors, and a quantitative resilience assessment to
52 o test experimentally whether any particular attractor architecture resides in any particular brain c
55 ed units express the spontaneous dynamics of attractor assemblies transitioning between distinct acti
57 dic memory [13-18], has been associated with attractor-based computations [5, 9], receiving support f
58 ene expression fluctuation occurs on or near attractor basin boundaries (the points of instability).
61 l, distal CA3 of aged rats may create weaker attractor basins that promote abnormal, bistable represe
63 y interneurons at the theta frequency causes attractor bumps to oscillate in speed and size, which gi
64 found in locusts can also operate as a ring attractor but differences in the inhibition pattern enab
66 demonstrate that the switching rate between attractors can be significantly influenced by the gene e
67 In case (iii), the dimension of the chaotic attractors can be very high, implying that the learning
70 These dynamics have led to the cancer cell attractor conceptual model, with implications for both c
71 t - a spiral - in which it behaved as a true attractor, converging to the same orbit when evoked, and
72 ssesses multiple metastable attractors, each attractor corresponding to a different spatial firing pa
75 mbles leading to destabilization of network "attractors" could be a defining aspect of neuropsychiatr
76 ess that converges to one of several precise attractors defining signatures representing biomolecular
77 ith the hypothesis that schizophrenia is an "attractor" disease and demonstrate that degraded neurona
78 be modeled using oscillatory interference or attractor dynamic mechanisms that perform path integrati
79 tive feedback loops, thereby elucidating the attractor (dynamic behavior) repertoire of the system an
80 on cognition by altering prefrontal cortical attractor dynamics according to an inverted U-shaped fun
81 human and monkey behavior show that discrete attractor dynamics account for the distribution, bias, a
82 ectly demonstrates that there are continuous attractor dynamics and enables powerful inference about
83 whether human memory retrieval is driven by attractor dynamics and what neural mechanisms might unde
86 between rhythmic firing patterns and complex attractor dynamics has implications for the interpretati
89 he hippocampal circuit and popular models of attractor dynamics in CA3 suggests a mechanistic explana
90 t is dramatically amplified by reverberating attractor dynamics in neural circuits for stimulus categ
93 n ambiguous novel context relate to putative attractor dynamics in the hippocampus, which support the
95 pace and offer experimental support for bump attractor dynamics mediating cognitive tasks in the cort
98 We consider the stochastic long-timescale attractor dynamics of pairs of mutually inhibitory popul
99 k of interacting head direction neurons, but attractor dynamics predict a winner-take-all decision be
100 an electrophysiology data, we show here that attractor dynamics that control neural spiking during mn
102 , to date, no demonstration exists that bump attractor dynamics underlies spatial working memory.
103 gh compression of graded feature encoding by attractor dynamics underlying stimulus maintenance and/o
104 se results is that sensory cortex implements attractor dynamics, although this proposal remains contr
105 eover, piriform odor representations exhibit attractor dynamics, both within and across trials, and t
106 ticity of sensory inputs, when combined with attractor dynamics, can reconcile self-movement informat
108 od reason to believe that the brain displays attractor dynamics, it has proven difficult to test expe
109 of general interest to neuroscience, such as attractor dynamics, temporal coding and multi-modal inte
117 twork dynamics possesses multiple metastable attractors, each attractor corresponding to a different
118 of theorized network structures called ring attractors elegantly account for these properties, but t
120 eakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages.
122 e models that feature a critical point as an attractor for the dynamics(10-15), the connection to rea
123 We show that the critical state becomes an attractor for these networks, which points toward the on
125 loped a neural network model of the CA3 with attractors for both position and discrete contexts.
126 as barriers and locally cooler areas act as attractors for trajectories, creating source and sink ar
127 te the location and strength of the midpoint attractor from species occurrence data sampled along mou
128 vity increased the stability around a stable attractor, globally quenching neural variability and cor
129 and time-delay phase maps of low dimensional attractors graphically depict the sequence between perio
130 -direction cells have been modeled as a ring attractor, grid cells as a plane attractor, and place ce
131 network models of GRNs and to compute their attractors impose specific assumptions that cannot be ea
134 states of complex nonlinear systems: stable attractors in deterministic models or modes of stationar
135 st whether memories are stored as multimodal attractors in populations of place cells, recent experim
138 defined and maintained by a wide variety of attractors including the complex tumor ecosystem and the
141 ntaining an unwanted beta-oscillation spiral attractor is controlled to function as a healthy motor s
143 ntly long delay times, the optimal number of attractors is less than the number of possible stimuli,
145 d, the stability of these states represents "attractor"-like states along a dynamic landscape that is
148 y cortex is organized into a small number of attractor-like neuronal assemblies, whose responses can
149 of a phase transition, and the emergence of attractor-like structure in the inferred energy landscap
150 ngle spatial map, position-dependent context attractors made transitions at different points along th
154 modeled subjects' behavior using a discrete attractor model and calculated within-subject correlatio
158 whether cell-cell relationships predicted by attractor models persist during sleep states in which sp
160 pure oscillatory interference and continuous attractor models, and provides testable predictions for
161 rid fields are produced by slow ramps, as in attractor models, whereas theta oscillations control spi
162 in PMd emerge from the coactivation of such attractor modules, heterogeneous in the strength of loca
163 nal transmission between a linked continuous attractor network and competitive network acts as a timi
164 ssociative memory model CA3 as a homogeneous attractor network because of its strong recurrent circui
165 s of grid-like maps were proposed, including attractor network dynamics, interactions with theta osci
166 previously developed biophysically detailed attractor network exhibits spontaneous oscillations in t
167 iophysically informed model of a competitive attractor network for decision making, we found that dec
169 bservations, combined with simulations of an attractor network grid cell model, demonstrate that land
171 cal simulations of a biophysical competitive attractor network model have shown that such a network c
173 s by considering an extension of the reduced attractor network model of Wong and Wang (2006), taking
175 id representation is unknown, but continuous attractor network models explain multiple fundamental fe
179 g firing field traversals, whereas competing attractor network models predict slow depolarizing ramps
181 Here, we discuss evidence for continuous attractor network models that account for grid firing by
183 cue interactions are thought to occur on an attractor network of interacting head direction neurons,
187 ly conflicting results are commensurate with attractor network theory, we developed a neural network
192 ippocampus has been postulated to be such an attractor network; however, the experimental evidence ha
193 natomical arrangement are suggestive of ring attractors, network structures that have been proposed t
197 ions, associative synaptic modification, and attractor networks in which the storage capacity is in t
199 y derive how the stored memory in continuous attractor networks of probabilistically spiking neurons
200 mes in the sequence, suggesting that spiking attractor networks of this type can support an efficient
203 aracteristic of decision states in recurrent attractor networks, and its possible relevance to consci
204 ften crucial for the stability of the single attractor networks, we have uncovered that the funneled
211 scenario for modeling memory function is the attractor neural network scenario, whose prototype is th
212 s, we consider a biophysical decision-making attractor neural network, taking into account an inhibit
214 decision-making, sharing a common recurrent (attractor) neural circuit mechanism with discrimination
215 diameter is proposed to be formed of a local attractor neuronal network with a capacity in the order
217 egafauna are arguably considered the primary attractor of ecotourists to sub-Saharan African protecte
226 en viewed as coming from transitions between attractors on an epigenetic landscape that governs the d
227 tion is not predicted by previous continuous attractor or oscillatory interference models of grid fir
228 ut being either trapped in the first reached attractor, or losing all memory of the past dynamics.
229 ions predicted that the network settles into attractors, or TF expression patterns, that correlate wi
230 luidic delivery to form precisely controlled attractor patterns and study the responses of these patt
231 rns in early development onto specific point attractor patterns in later development are essentially
232 an likewise produce precise patterns, termed attractor patterns, that reform their precise shape afte
233 d cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagon
234 pped as dynamical states clustered around an attractor point in gene expression space, owing to a bal
235 gree distribution and the number of periodic attractors produced determine the relative complexity of
238 r autoregressive algorithm uses multivariate attractors reconstructed as the inputs of a neural netwo
243 el that demonstrates that alternative stable attractors, representing the ictal and postictal states,
244 athematical model to capture such biological attractor selection and derive a generic, adaptive and d
245 We show that the proposed scheme based on attractor selection can not only promote the balance of
247 nd provides a deep understanding of adaptive attractor selection-based control formation that is usef
248 with similar preferred directions as a ring attractor, so that their relative phases remain constant
250 increases in monoamine efflux would enhance attractor stability, whereas high frontal monoamine leve
251 ne networks self-organize, either into point attractors (stable repeating patterns of gene expression
253 he destabilization of their high-dimensional attractor state, such that differentiating cells undergo
258 to calculate rates of switching between two attractor states and enables an accurate simulation of t
260 ) code of transcription factors that produce attractor states in the underlying gene regulatory netwo
261 l code of transcription factors that produce attractor states in the underlying gene regulatory netwo
262 eterogeneity can be specified dynamically by attractor states of a master regulatory TF network.
263 tive responses, as well as the robustness of attractor states of networks of neurons performing memor
266 ble, both in time and space, indicating that attractor states were still present despite the lack of
270 mor stage, a mitotic chromosomal instability attractor strongly associated with tumor grade, and a ly
271 fined in all cases: a mesenchymal transition attractor strongly associated with tumor stage, a mitoti
272 d be an integrator of inputs into a bistable attractor switching between two highly trusted interpret
273 y-based analyses to reveal the longest-known attractor system in mammalian biology underlying the met
275 I propose an alternate mechanism to a line attractor that allows the network to hold the value of a
276 directed motion mode resembles a limit cycle attractor that is independent of its initial condition.
277 ate during a trial suggests that the type of attractor that is responsible for holding the stimulus i
278 le the probability of the system being in an attractor that lies within prescribed boundaries decreas
280 These are called the fixed-point chaotic attractor, the fixed-point strange nonchaotic attractor,
281 m offers a substantial advantage over a line attractor: The tuning requirements of cell to cell conne
282 continuously changed states within their own attractor, thus driving the repopulation, as shown by fl
283 er perturbation to drive the system from one attractor to another, assuming that the former is undesi
284 ceptualized as automatic, bottom-up resource attractors to on-beat times-preparatory neural activity
285 emory rely on finely tuned, content-specific attractors to persistently maintain neural activity and
286 lity of their gene expression configuration (attractor) to exit the attractor in one direction remain
287 features to disease prediction, we find that attractor topography of nutrient metabolism is altered i
288 is proposed in which meta-stable sequential attractor transitions are learned through changes to syn
289 ulating Boolean network models and obtaining attractors under different assumptions by successfully r
290 the mechanisms that move the system between attractors using both the quasipotential and the probabi
291 hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network stat
292 It is used nonlinear dynamics tools to find attractors, which bound the motion of the spacecraft.
293 twork contains the core components of a ring attractor while also revealing unpredicted structural fe
295 The system periodically switches between one attractor with a fixed single-well potential and the oth
296 networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to
299 large set of networks can give rise to four attractors with the stepwise regulations of transcriptio
300 memory can be supported by overlapping local attractors within a spatial map of CA3 place cells.
302 biological diversity and that the number of attractors within the phase space exponentially increase