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.

Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to “reconstruct” some supposed influences. In the 1970s, a new way of performing science under the name “chaos” emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a direct testimony of how contributors can be influenced by other scientists or works, we here collected some writings about the early times of a few contributors to chaos theory. The purpose is to exhibit the diversity in the paths and to bring some elements—which were never published—illustrating the atmosphere of this period. Some peculiarities of chaos theory are also discussed.

In this paper, we propose a new method based on the dynamic mode decomposition (DMD) to find a distinctive contrast between the ictal and interictal patterns in epileptic electroencephalography (EEG) data. The features extracted from the method of DMD clearly capture the phase transition of a specific frequency among the channels corresponding to the ictal state and the channel corresponding to the interictal state, such as direct current shift (DC-shift or ictal slow shifts) and high-frequency oscillation (HFO). By performing classification tests with Electrocorticography (ECoG) recordings of one patient measured at different timings, it is shown that the captured phenomenon is the unique pattern that occurs in the ictal onset zone of the patient. We eventually explain how advantageously the DMD captures some specific characteristics to distinguish the ictal state and the interictal state. The method presented in this study allows simultaneous interpretation of changes in the channel correlation and particular information for activity related to an epileptic seizure so that it can be applied to identification and prediction of the ictal state and analysis of the mechanism on its dynamics.