Dynamic link of memory—Chaotic memory map in nonequilibrium neural networks

Tsuda, Ichiro

doi:10.1016/s0893-6080(05)80029-2

Cited by 324 publications

(110 citation statements)

References 43 publications

Supporting

Mentioning

101

Contrasting

Unclassified

Order By: Relevance

“…A macrovariable, related to the "activity" of the network (see figure 1, similar plots appeared also in [12] and [18]) was observed to evolve as a noisy one dimensional map in the case that the network receives no external stimulus. 4 This was regarded in [18] as a rule of successive association of memory, exhibiting chaotic dynamics.…”

Section: A Neuroscientifically Motivated Examplesupporting

confidence: 59%

See 1 more Smart Citation

Chaotic Itinerancy in an Associative Memory Model

Galatolo¹,

Monge²,

Marangio³

et al. 2018

Preprint

View full text Add to dashboard Cite

We consider a random dynamical system arising in a model of associative memory. This system can be seen as a small (stochastic and deterministic) perturbation of a determinstic system having two weak attractors which are destroyed after the perturbation. We show, with a computer aided proof, that the system has a kind of chaotic itineracy. Typical orbits are globally chaotic, while they spend relatively long time visiting attractor's ruins.

show abstract

Section: A Neuroscientifically Motivated Examplesupporting

confidence: 59%

“…4 This was regarded in [18] as a rule of successive association of memory, exhibiting chaotic dynamics.…”

Section: A Neuroscientifically Motivated Examplementioning

confidence: 99%

Chaotic Itinerancy in an Associative Memory Model

Galatolo¹,

Monge²,

Marangio³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, to obtain chaotic transitions, a quasi-attractor should not be stabilized, at least, in the sense of linear stability. Then, in a neighborhood of a quasi-attractor, the dynamics begin from at least the second order, because of the linear term vanishing; dx/dt = bx 2 -- Fig. 1--The dynamic process and its transition rule were studied in a recurrent network with excitatory neurons, each receiving inhibitory signals, a structure found in common in both the neocortex and the hippocampus, and a circle map with criticality as a transition rule was found.…”

Section: Communicating Brainsmentioning

confidence: 99%

“…1--The dynamic process and its transition rule were studied in a recurrent network with excitatory neurons, each receiving inhibitory signals, a structure found in common in both the neocortex and the hippocampus, and a circle map with criticality as a transition rule was found. The criticality was robust for changing network parameters [1,2]. Here, criticality appeared in two ways: a circle map was in a critical stage between a chaotic map and a stable one, and fixed points representing memories were Milnor attractors but not conventional ones.…”

Section: Communicating Brainsmentioning

confidence: 99%

See 1 more Smart Citation

Chaotic itinerancy and its roles in cognitive neurodynamics

Tsuda

2015

Current Opinion in Neurobiology

Self Cite

View full text Add to dashboard Cite

Chaotic itinerancy is an autonomously excited trajectory through high-dimensional state space of cortical neural activity that causes the appearance of a temporal sequence of quasi-attractors. A quasi-attractor is a local region of weakly convergent flows that represent ordered activity, yet connected to divergent flows representing disordered, chaotic activity between the regions. In a cognitive neurodynamic aspect, quasi-attractors represent perceptions, thoughts and memories, chaotic trajectories between them with intelligent searches, such as history-dependent trial-and-error via exploration, and itinerancy with history-dependent sequences in thinking, speaking and writing.

show abstract

On Recursive Production and Evolvability of Cells: Catalytic Reaction Network Approach

Kaneko

2005

Geometric Structures of Phase Space in Multidimensional Chaos

View full text Add to dashboard Cite

To unveil the logic of cell from a level of chemical reaction dynamics, we need to clarify how ensemble of chemicals can autonomously produce the set of chemical, without assuming a specific external control mechanism. A cell consists of a huge number of chemical species that catalyze each other. Often the number of each molecule species is not so large, and accordingly the number fluctuations in each molecule species can be large. In the amidst of such diversity and large fluctuations, how can a cell make recursive production? On the other hand, a cell can change its state to evolve to a different type over a longer time span. How are reproduction and evolution compatible? We address these questions, based on several model studies with catalytic reaction network.In the present survey paper, we first formulate basic questions on the recursiveness and evolvability of a cell, and then state the standpoint of our research to answer the questions, that is termed as 'constructive biology'. Based on this standpoint, we present general strategy of modeling a cell as a chemical reaction network.At the first part we investigate of the origin of heredity in a cell, by noting that the molecules carrying heredity must be preserved well and control the behavior of a cell. We take a simpled model consisting of two mutually catalyzing molecule species, each of which has catalytically active and inactive types. One of the molecule species is synthesized slowly, and thus is a minority in population. Through the growth and division of this cell, it is shown to reach and remain in a state in which a active, minority molecules are preserved over generations, and control the cell behavior. This minority controlled state is achieved by preserving rare number fluctuations of molecules. The state gives rise to a selection pressure for mechanisms that ensure the transmission of the minority molecule. The minority molecule, thus, carries heredity, and is a candidate for "genetic information". Experimental confirmation of this minority control is also presented.Next, a protocell model consisting of a large number mutually catalyzing molecule species is studied, in order to investigate how chemical compositions are transferred recursively under replication errors. Depending on the numbers of molecules and species in a cell, and the path rate in the reaction network, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. At a recursive production state chemicals are found to form intermingled hypercycle network that consists of core hypercycle and peripheral network that influence each other. How this intermingled network supports the recursive production, and how minority in the core hypercycle gives rise to a switch to other recursive states at the itinerancy phase are elucidated. Evolution of this hypercycle network is also studied, to show the approach to recursive production of cells and switch to more efficient reproduction states. Finally, statistic...

show abstract

Dynamic link of memory—Chaotic memory map in nonequilibrium neural networks

Cited by 324 publications

References 43 publications

Chaotic Itinerancy in an Associative Memory Model

Chaotic Itinerancy in an Associative Memory Model

Chaotic itinerancy and its roles in cognitive neurodynamics

On Recursive Production and Evolvability of Cells: Catalytic Reaction Network Approach

Contact Info

Product

Resources

About