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We present three curious phenomena in coupled chaotic systems with different time scales: a copy, an itinerant motion, and a “firework.” The phenomena obtained may possibly have implications on the interaction between two macroscopic systems, namely the “observing” and the “observed” systems.

Although the role of corticopetal acetylcholine (ACh) in higher cognitive functions is increasingly recognized, the questions as (1) how ACh works in attention(s), memory dynamics and cortical state transitions, and also (2) why and how loss of ACh is involved in dysfunctions such as visual hallucinations in dementia with Lewy bodies and deficit of attention(s), are not well understood. From the perspective of a dynamical systems viewpoint, we hypothesize that transient ACh released under top‐down attention serves to temporarily invoke attractor‐like memories, while a background level of ACh reverses this process returning the dynamical nature of the memory structure back to attractor ruins (quasi‐attractors). In fact, transient ACh loosens inhibitions of py ramidal neurons (PYRs) by P V+ fas t spiking (FS) i nterneurons, while a baseline ACh recovers inhibitory actions of P V+ FS. Attentional A Ch thus dynamically modifies brain’s connectivity. Th e core of this process is in the depression of GABAergic ...

In this paper, four spatiotemporal coding mechanisms in the CA3‐CA1were examined.In this paper, four spatiotemporal coding mechanisms in the CA3‐CA1were examined.

A new method for computing the largest Lyapunov exponent from chaotic time series is presented, whereby more robust convergence to the exact value is obtained. It aims to serve as a bridge between the two widely known existing methods: the Wolf and the Jacobian methods.

We report herein a rare case of primary lung cancer that occurred concomitantly with the calcified ova of a parasite. A 58-year-old man was referred to our department after a pulmonary abnormal shadow had been seen on a chest X-ray done at mass screening. A transbronchial lung biopsy (TBLB) revealed the calcified ova of a parasite. Because the possibility of concomitant lung cancer could not be ruled out, a lung biopsy was taken via video-assisted thoracic surgery (VATS). The pathological diagnosis was squamous cell carcinoma, and a left upper lobectomy was serially performed through a posterolateral thoracotomy. The patient recovered uneventfully and has remained in good health without any sign of recurrence for over 9 months. Following this case report, we review three other cases of this unusual disease combination documented in the literature.

Cortical layer 1 is the main entrance of top-down signals from other higher cortices and subcortical nuclei. Recent findings challenge the view that top-down signals play just a modulatory role. However, how top-down signals are implemented to help reconstruct the internal representations of images, or an episode of events is poorly understood. Recent experimental data suggest that the “ongoing” brain state without external inputs into layer 4 and attentional top-down signals continually fluctuates among the intrinsic patterns of activity. Viewed from a dynamical systems standpoint, the transitory intrinsic states could be an expression of “attractor ruins”, observed in a mesoscopic dynamical system. We hypothesize that when top-down signals arrive as attention(s), contexts, or indices, the local brain state is temporarily stabilized to be an attractor(-like) state. In view of the anatomical and physiological configurations of neuronal systems in the superficial layers, we propose a hypothetical scenario for such non-classical dynamics in the brain.

Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ a mechanism of encoding sequences of events. The “Cantor coding” hypothesis in hippocampal CA1 has been proposed, which provides a scheme for encoding temporal sequences of events. Here, in order for investigating the Cantor coding in detail, we constructed a model for the CA1 network which consists of conductance-based model neurons. It was assumed that the CA3 outputs temporal sequences of spatial patterns to CA1. It was shown that the output patterns of CA1 were hierarchically clustered in a self-similar manner according to the similarity of input time series. The dependency of the efficacy of encoding on the input time interval and its robustness against noise was investigated.

The hippocampus has been considered responsible for the formation of episodic memory. It has also been pointed out that the hippocampus plays an important role in imagination, which is related to future events. The fact that atrophy of the hippocampus could lead to Alzheimer’s disease implies that the network structure of the hippocampus may provide fields for the creation of internal time corresponding to the past, present, and future. We present a hypothesis that the hippocampus plays a role in the formation of self-identity via interactions with the lateral prefrontal cortex.

In rat CA1 pyramidal cells, we previously observed hierarchical clusters of the distribution of membrane potentials, arranged according to the history of input sequences. In this study, we deal with the dynamical mechanism generating such a hierarchical distribution. The recording data were investigated using return map analysis. Each of the obtained return maps was well approximated by a set of contractive affine transformations. These findings provide direct evidence that the information of temporal sequences generated in CA3 can be self-similarly represented in the membrane potentials of CA1 pyramidal cells.

We found a chaotic pulsation in a finger’s capillary vessels in both normal subjects and psychiatric patients, as well as cardiac chaos. A proof of chaos was made by the reconstruction of the dynamics in phase space and the calculation of the Lyapunov exponents. From the aspect of chaotic information processing, we give a measure of the information storage capacity of the observed chaos. We also found a difference in the topology of capillary and cardiac chaos, and a difference in their dependence on the subject’s conditions.

How does the information of spatiotemporal sequence stemming from the hippocampal CA3 area affect the postsynaptic membrane potentials of the hippocampal CA1 neurons? In a recent study, we observed hierarchical clusters of the distribution of membrane potentials of CA1 neurons, arranged according to the history of input sequences (Fukushima et al Cogn Neurodyn 1(4):305–316, 2007). In the present paper, we deal with the dynamical mechanism generating such a hierarchical distribution. The recording data were investigated using return map analysis. We also deal with a collective behavior at population level, using a reconstructed multi-cell recording data set. At both individual cell and population levels, a return map of the response sequence of CA1 pyramidal cells was well approximated by a set of contractive affine transformations, where the transformations represent self-organized rules by which the input pattern sequences are encoded. These findings provide direct evidence that the information of temporal sequences generated in CA3 can be self-similarly represented in the membrane potentials of CA1 pyramidal cells.

In contrast to the conventional static view of the brain, recent experimental data show that an alternative view is necessary for an appropriate interpretation of its function. Some selected problems concerning the cortical transitory dynamics are discussed. For the first time, we propose five scenarios for the appearance of chaotic itinerancy, which provides typical transitory dynamics. Second, we describe the transitory behaviors that have been observed in human and animal brains. Finally, we propose nine hypotheses on the functional roles of such dynamics, focusing on the dynamics embedded in data and the dynamical interpretation of brain activity within the framework of cerebral hermeneutics.

We propose a new dynamical mechanism for information processing in mind and brain. We emphasize that a hermeneutic process is one of the key processes manifesting the functions of the brain and that it can be formulated as an itinerant motion in ultrahigh dimensional dynamical systems, which may give a new realm of the dynamic information processing. Our discussions are based on the notion of chaotic information processing and the observations of biological chaos.

The Role(s) of corticopetal acetylcholine (ACh) in perception and conscious flow is largely unknown. The attention hypothesis may well be established experimentally. The aim of this talk is to give a small review, and then try to extend further the arguments, on the role of corticopetal ACh in perception from a dynamical systems standpoint, to search for its possible role in perceptual binding, and in the transient genesis of quasi-attractors through the mechanism of changing synchrony.

2008-32-0010 (SAE) / 20084710 (JSAE), We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual engine system. The experimental results show that the chaotic motion of an engine system may be stabilized to a periodic motion. Alternatively, harnessing chaos for engine systems is addressed, which regards chaos as an essential dynamic mode for the engine.

The hippocampus, which is a part of the old brain, has been considered responsible for the formation of episodic memory. Atrophy of the hippocampus can lead to Alzheimer disease. Alzheimer disease is a problem of the society. It is also expected to pose a serious problem in future societies composed of large numbers of elderly people. Therefore, it has become the focus of considerable attention. Motivated by the rehabilitation process of Alzheimer's patients, we mathematically studied the coding scheme in the hippocampus. We show that a mathematical model for CA3 exhibits successive recalls of memories which follow the emergent chaotic dynamics, where chaotic dynamics means ordered but comple and unpredictable neural activity. We also show that a network consisting of two-compartment model neurons for CA1 produces Cantor sets, by which the input time series of CA1 can be hierarchically encoded. We called this coding scheme Cantor coding. Predictions obtained from the model study have been partially verified by experiments using rat hippocampal slices.

To adapt to changeable or unfamiliar environments, it is important that animals develop strategies for goal-directed behaviors that meet the new challenges. We used a sequential paired-association task with asymmetric reward schedule to investigate how prefrontal neurons integrate multiple already-acquired associations to predict reward. Two types of reward-related neurons were observed in the lateral prefrontal cortex: one type predicted reward independent of physical properties of visual stimuli and the other encoded the reward value specific to a category of stimuli defined by the task requirements. Neurons of the latter type were able to predict reward on the basis of stimuli that had not yet been associated with reward, provided that another stimulus from the same category was paired with reward. The results suggest that prefrontal neurons can represent reward information on the basis of category and propagate this information to category members that have not been linked directly with any experience of reward.

This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation in embryos and functional differentiation in cortical modules are typical examples of this phenomenon. In this paper, as case studies, we deal with three mathematical models that yielded components via such global constraints: the genesis of neuronal elements, the genesis of functional modules, and the genesis of neuronal interactions. The overall development of a system may follow a certain variational principle.

To clarify how the information of spatiotemporal sequence of the hippocampal CA3 affects the postsynaptic membrane potentials of single pyramidal cells in the hippocampal CA1, the spatio-temporal stimuli was delivered to Schaffer collaterals of the CA3 through a pair of electrodes and the post-synaptic membrane potentials were recorded using the patch-clamp recording method. The input–output relations were sequentially analyzed by applying two measures; “spatial clustering” and its “self-similarity” index. The membrane potentials were hierarchically clustered in a self-similar manner to the input sequences. The property was significantly observed at two and three time-history steps. In addition, the properties were maintained under two different stimulus conditions, weak and strong current stimulation. The experimental results are discussed in relation to theoretical results of Cantor coding, reported by Tsuda (Behav Brain Sci 24(5):793–847, 2001) and Tsuda and Kuroda (Jpn J Indust Appl Math 18:249–258, 2001; Cortical dynamics, pp 129–139, Springer-Verlag, 2004).

We review basic concepts of dynamical systems in the first half of this article. In the second half, we focus on cortical transitory dynamic behaviors observed during task-related actions of animals, and provide a dynamical interpretation of such transitory behaviors in terms of chaotic itinerancy.

By re-examining the neuronal activity energy model, we show the inadequacies in the current understanding of the energy consumption associated with neuron activity. Specifically, we show computationally that a neuron first absorbs and then consumes energy during firing action potential, and this result cannot be produced from any current neuron models or biological neural networks. Based on this finding, we provide an explanation for the observation that when neurons are excited in the brain, blood flow increases significantly while the incremental oxygen consumption is very small. We can also explain why external stimulation and perception emergence are synchronized. We also show that negative energy presence in neurons at the sub-threshold state is an essential reason that leads to blood flow incremental response time in the brain rather than neural excitation to delay.

Patients with critically ischemic limbs due to maintenance hemodialysis and diabetes are increasing in number markedly in Japan. The difficulty of treating critically ischemic limbs is well recognized. Despite active medication and surgical therapy, many critically ischemic limbs are amputated. Ninety-two patients with critically ischemic limbs were treated by transplantation of autologous peripheral blood stem cells (PBSCs). The stem cells were mobilized into the peripheral blood by administration of granulocyte colony stimulating factor (G-CSF). The mobilized mononuclear cells were separated by an apheresis technique using a centrifuge. The separated mononuclear cells contained approximately 4.0 x 10(7) CD34-positive cells. The collected cell suspension was divided into aliquots of 0.5-1.0 ml and transplanted into the muscle of ischemic limbs at 50-70 transplantation points. At 1.5 months after PBSC transplantation, a strong immunostaining of CD34-positive cells and factor VIII, as well as capillary formation, was observed in the muscles into which stems cells had been transplanted. In each patient tested, the serum vascular endothelial growth factor (VEGF) level increased after stem cell transplantation; the mean VEGF level increased by 176%. Of 11 diabetic patients (DM) who were not receiving hemodialysis (HD), there were no amputees regardless of their Fontaine classification. Of 19 patients in the HD(+)DM(-) category, there were no amputations in Fontaine stage I, II, and III patients, whereas three limbs and one toe were amputated in Fontaine stage IV patients. Of 13 patients in the HD(-)DM(+) category, none of the Fontaine stage I, II, or III patients underwent amputation, but six Fontaine stage IV patients underwent amputation. Of 49 patients in the HD(+)DM(+) category, 38 (78%) were classified as Fontaine stage IV, 71% (27/38) of whom had a toe or a limb amputated. In nine patients over 80 years of age, one toe and one limb were amputated. Nondiabetic, nondialyzed patients with ischemic limbs are strongly indicated for stem cell transplantation regardless of Fontaine classification. Therapeutic angiogenesis is effective for critically ischemic limbs resulting from hemodialysis and diabetes until Fontaine stage III, but is of limited effectiveness for stage IV cases.

We propose a framework of neurocognitive experiments that clarifies structures of descriptions for the observed data. This framework can be used to determine the limitation of their possible interpretations and to reveal tacit assumptions of the experiments. We apply the framework to some actual neurocognitive experiment whose aim was to clarify internal inference processes of animals, and we also examine possible processes which the observer can describe in this framework. We show that our framework predicts the existence of unidentified types of neurons, thereby the framework can be used to propose new types of experiments.

Interneurons may function as coordinator of cortical dynamics, as "super networks" driven by top down signals. Dynamical systems-theoretic view on cortical dynamics and its hypothetical cognitive roles are discussed. In particular, we discuss three related issues concerning the cognitive role of inhibitory interneurons in the neocortex. 1) Theoretical possibility of emergence of transient synchrony in chaotic itinerant dynamics in gap junction-coupled interneuron networks; 2) Dynamical systems-theoretic, and nonclassical memory view based on the concept of Milnor attractor; and 3) A new hypothesis on functional role of activity-dependent depolarizing action of GABAA in inhibitory interneurons

The non-classical, but frequently reported behavior of GABA[A] receptor-mediated excitation in mature CNS has long been regarded as a puzzle. We theorize that the function of cortical GABAergic interneurons, which might constitute a subsystem of brain's GABA interneurons, is their ability of switching from inhibitory action to excitatory action depending on the level of spatio-temporal activity in progress. From the perspective of a dynamical systems approach, such "excitatory" GABAergic responses may serve to temporarily invoke attractor-like memories when extensively activated by, for example, top-down signals as category information or attention, while an ongoing background state of GABA changes its action to inhibition, returning the dynamical nature of the memory structure back to attractor ruins., http://www.worldscinet.com/jin/jin.shtml

We report the existence of chaotic itinerancy in a coupled Milnor attractor system. The attractor ruins consist of tori or local chaos generated from the original Milnor attractors. The chaotic behavior exhibited by a single orbit can be considered a “nonstationary” state, due to the extremely slow convergence of the Lyapunov exponents, but the behavior averaged over randomly chosen initial conditions is consistent with the limit theorem. We present as a possibly new indication of chaotic itinerancy the presence of slow decay of large fluctuations of the largest Lyapunov exponent.

We investigate the dynamic character of a network of electrotonically coupled cells consisting of class I point neurons, in terms of a finite dimensional dynamical system. We classify a subclass of class I point neurons, called class I* point neurons. Based on this classification, we use a reduced Hindmarsh-Rose (H-R) model, which consists of two dynamical variables, to construct a network model consisting of electrotonically coupled H-R neurons. Although biologically simple, the system is sufficient to extract the essence of the complex dynamics, which the system may yield under certain physiological conditions. The network model produces a transitory behavior as well as a periodic motion and spatio-temporal chaos. The transitory dynamics that the network model exhibits is shown numerically to be chaotic itinerancy. The transitions appear between various metachronal waves and all-synchronization states. The network model shows that this transitory dynamics can be viewed as a chaotic switch between synchronized and desynchronized states. Despite the use of spatially discrete point neurons as basic elements of the network, the overall dynamics exhibits scale-free activity including various scales of spatio-temporal patterns., http://www.worldscinet.com/jin/jin.shtml

We present a neural model for a singular-continuous nowhere-differentiable (SCND) attractors. This model shows various characteristics originated in attractor's nowhere-differentiability, in spite of a differentiable dynamical system. SCND attractors are still unfamiliar in the neural network studies and have not yet been observed in both artificial and biological neural systems. With numerical calculations of various kinds of statistical quantities in artificial neural network, dynamical characters of SCND attractors are strongly suggested to be observed also in neural systems experiments. We also present possible information processings with these attractors.

In physics, we are used to adopting a descriptive approach of nature. Often, one might assume that the macroscopic level of nature can be understood based on an understanding of the microscopic level. For example, the following chart flow is often applicable.

Let us call a machine involving simple stimulus-response rules a Cartesian automaton, and call a Cartesian automaton possessing a control system including feedback systems a Craik automaton [Johnson-Laird 1983]. By the studies of Karl von Frish, it turned out that a honey bee calculates the positions of flowers in relation to the position of the sun, and correctly sends such information to other bees. This seems to be a kind of sophisticated information processing, but its processing mechanism is essentially the same as that of a Craik automaton. The reason is as follows. Once the control system is set up, it performs correct calculations and outputs the results correctly, based on the present state and the purpose. In other words, the same result is output, provided the conditions are the same.

In this final chapter we would like to review the current book by organizing the issues and novel viewpoints in aseries of question and answer sessions with the editors.

If chaos could be characterized by one word, it would be “complexity”. Even with the greatest of efforts, a finite sequence cannot accurately describe chaos. Chaos can be perfectly represented only in an infinite sequence. Several problems stemming from the discrepancy between this infiniteness and the finiteness of observation and description will be discussed later, but here we briefly touch upon it.

As an example of the high-dimensional dynamics discussed in Chap. 1, let us consider a network of chaotic elements. In a network system many elements that can display chaotic dynamics interact with each other and evolve in time. Here we introduce the globally coupled map (GCM) as the simplest example of such a network of chaotic elements. We discuss the observed phenomena and th e universal concepts revealed therein in some detail, since the model provides us with a ‘dynamic many-to-many relationship’, ‘constructive model’, and ‘dynamics between the whole and its parts’. We believe that through the study of the GCM, we can work towards a methodology studying complex systems.

The complexity theory of interactions among functional levels in brain is developed. In particular, a possible interplay between the logical process and the sensory information processings is highlighted. In this respect, we deal with the transformation between a logical statement and a dynamical system, in relation with dynamics of neurons or neural assemblies. Both internal and external views for the threshold or the switching mechanism of neuron is discussed. An external view is generally represented by dynamical systems, which is assured here by the plausibility of conventional population dynamics. The internal view in the present context is assured by the existence of logical process of macromolecules in the pre- and/or post-synaptic membranes of neuron. Thus the internal view provides logic-based dynamics. There always exist two interpretations for the logic-based dynamics, which lead internal and external dynamics, respectively. The internal dynamics brings about the threshold-related characteristics of neuron, clue to its chaotic behaviors, whereas the external one provides a periodic behavior only. With this internal theory, we develop the hermeneutic theory for interfacial dynamics of different levels of neural assemblies, and for the notion of stability of self-description.

Basic problems of complex systems are outlined with an emphasis on irreducibility and dynamic many-to-many correspondences. We discuss the importance of a constructive approach to artificial reality and the significance of an internal observer., Comment: 11 pages; Physica D, in press

In this paper, we study a dynamic structure of discretized vector fields obtained from the Brusselator, which is described by two-dimensional ordinary differential equations (ODEs). We found that a bifurcation structure of the logistic map is embedded in the discretized vector field. The embedded bifurcation structure was unraveled by the dynamical orbits that eventually converge to a fixed point. We provide a detailed mathematical analysis to explain this phenomenon and relate it to the solution of the original ODEs.