Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among “exotic” attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given.

Chaotic dynamics can be related to analog computation. A possibility of electronically implementing the chaos-driven contracting system in the target article is explored with an analog electronic circuit with inevitable noise from the viewpoint of analog computation with chaotic neurons.

The framework within which Tsuda proposes his solution for transitory dynamics between attractor states is flawed from a neurological perspective. We present a more genuine framework and discuss the roles that external input and synaptic modulations play in the evolution of the dynamics of neuronal systems. Chaotic itinerancy, it is argued, is not necessary for transitory dynamics.

Experimental evidence and mathematical/computational models show that in many cases chaotic, nonregular oscillations are adequate to describe the dynamical behaviour of neural systems. Further work is needed to understand the meaning of this dynamical regime for modelling information processing in the brain.

Tsuda examines the potential contribution of nonlinear dynamical systems, with many degrees of freedom, to understanding brain function. We offer suggestions concerning symmetry and transients to strengthen the physiological motivation and theoretical consistency of this novel research direction: Symmetry plays a fundamental role, theoretically and in relation to real brains. We also highlight a distinction between chaotic “transience” and “itineracy.”

Single cell receptive field dynamics characterized by highly complicated spatio-temporal activity distributions observable during sensory information processing transforms into much simpler spatio-temporal activity pattern at a population level, indicating a qualitative transformational step of time-variant processing from microscopic to mesoscopic levels. As these dynamics are subject to significant modifications during learning, dynamic information processing is in a permanent state of use-dependent fluctuations.

Philosophical, dynamical, neural, network-theoretical, and cognitive ingredients of Tsuda's brain theory are discussed and anayzed. The integrative approach emphasized by Tsuda would be a welcome one.

This commentary provides a critique of Tsuda's target article, focusing on the hippocampus and episodic long-term memory. More specifically, the relevance of Cantor coding and chaotic itinerancy for long-term memory functioning is considered, given what we know about the involvement of the hippocampus in the mediation of long-term episodic memory (based on empirical neuroimaging studies and investigations of brain-damaged amnesic patients).

Tsuda offers advanced concepts to model brain functions, includ-ing “chaotic itinerancy,” “attractor ruins,” “singular-continuous nowhere-differentiable attractors,” “Cantor coding,” “multi-Milnor attractor systems,” and “dynamically generated noise.” References to physiological descriptions of attractor landscapes governing activity over cortical fields maintained by millions of action potentials may facilitate their application in future experimental designs and data analyses.

Neurally inspired models of human cognition exude explanatory power without necessarily making predictions that can be verified behaviorally. This is the case for Tsuda's dynamic model. It is suggested that a simpler principle based on the nonlinear dynamic interaction between modules based on control of chaos, can achieve a similar theoretical goal in a cognitively verifiable way.

Memory dynamics need both stable and unstable properties simultaneously. Hence memory dynamics cannot be simulated by chaotic itinerant dynamics alone, with no real world correspondence. Memory dynamics are constrained by both semantics and causalities in the embodied cognition.

When theoreticians talk about noise, they frequently forget about the idealization coupled with this term. Another implicit and rarely mentioned assumption is that the tools of mathematics used are idealizations, too. Though some of Tsuda's ideas are similar to mine (e.g., we both believe that nonlinearity is one of the main reasons why the brain works the way it does; Kowalik et al. 1996), some critical remarks are in order.

Chaotic itinerancy is useful for illustrating transitions in attractor dynamics seen in the olfactory system. Cantor coding is a good model for information processing, but so far it lacks perceptual proof. The theories presented provide a large step toward bridging the use of chaos as an interpretive tool and hard examination of chaotic neural activity during perception.

Spatio-temporal neuro-dynamics is a quickly developing field of brain research and Tsuda's work is a significant contribution toward establishing theoretical foundations in this area. It is conceivable that the fragmented attractor landscapes and dynamical memory patterns identified earlier in various K-sets are biologically plausible manifestations of attractor ruins, chaotic itinerancy, and Cantor encoding as applied to sensory information processing.

The dynamical view of the brain that Tsuda presents is thoroughly substantiated by theory and computer simulations, but strong experimental evidence for chaotic brain processes is still lacking. New methods are called for. It is also important to make a distinction between the generating mechanisms and the observed behavior, which is complicated by a mixing of stochastic and deterministic processes.

Studies have failed to yield definitive evidence for the existence and/or role of well-defined chaotic attractors in real brain systems. Tsuda's transients stabilized on unstable manifolds of unstable fixed points using mechanisms similar to Ott's algorithmic “control of chaos” are demonstrable. Grebogi's order in preserving “strange nonchaotic” attractor with fractal dimension but Lyapounov is suggested for neural network tasks dependent on sequence.

We discuss whether low-dimensional chaos and even nonlinear processes can be traced in the electrical activity of the brain. Experimental data show that the dimensional complexity of the EEG decreases during event-related potentials associated with cognitive effort. This probably represents increased nonlinear cooperation between different neural systems during sensory information processing.

After critical appraisal of mathematical and biological characteristics of the model, we discuss how a classical hippocampal neural network expresses functions similar to those of the chaotic model, and then present an alternative stimulus-driven chaotic random recurrent neural network (RRNN) that learns patterns as well as sequences, and controls the navigation of a mobile robot.

Tsuda's article suggests several plausible concepts of neurodynamic representation and processing, with a thoughtful discussion of their neurobiological grounding and formal properties. However, Tsuda's theory leads to a holistic view of brain functions and to the controversial conclusion that the “binding problem” is a pseudo-problem. By contrast, we stress the role of chaotic patterns in solving the binding problem, in terms of flexible temporal coding of visual scenes through graded and intermittent synchrony.

I question whether chaotic itinerancy is anything new or different to existing research on heteroclinic cycles (cycling-chaos), and blow-out bifurcations (attractor-bubbling) that provide more detailed and better definition for nonlinear phenomena occurring in neural systems. I give a brief description of this research for comparison and expansion, and see it as an important component in dynamical models of neural activity.