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Domains of cooperative neural activity called "wave packets" have been discovered in the visual, auditory, and somatomotor cortices of rabbits that were trained to discriminate conditioned stimuli in these modalities. Each domain forms by a first order state transition, which strongly resembles a phase transition from vapor to liquid. In this view, raw sense data injected into cortex by sensory axons drive cortical action potentials in swarms like water molecules in steam. The increased activity destabilizes the cortex. Within 3 to 7 milliseconds of transition onset, the activity binds together into a state resembling a scintillating rain drop, which lasts ~80 to 100 milliseconds, then dissolves. Wave packets form at rates of 2 to 7/second in all sensory areas, overlapping in space and time. Results of sensory information processing are seen in spatial patterns of amplitude modulation (AM) of wave packets with carrier waves in the gamma range (20 to 80 Hz in rabbits). The AM patterns correspond to categories of CSs that the rabbits can discriminate. The patterns are found in electroencephalographic (EEG) potentials generated by dendrites and recorded with high-density electrode arrays. The state transitions by which AM patterns form are manifested in the spatial pattern of phase modulation (PM), which have the radial symmetry of a cone. The apex of a PM cone marks the site of nucleation of an AM pattern. The phase gradient gives a soft boundary condition, where the axonal delay in spread gives sufficient phase dispersion to reach the half-power level. The size of the wave packets (10 to 30 mm in diameter in rabbits) is determined largely by the conduction velocities of intracortical axons through which the neural cooperation is maintained. The findings show that significant cortical activity takes the form of mesoscopic interactions of millions of neurons in broad areas of cortex, which are more clearly detected in graded dendritic potentials than in action potentials. The distinction is analogous to the difference between statistical mechanical and thermodynamic descriptions of particle behavior. Both types of neural activity show spatial and temporal discontinuities but at distinctive scales of microns and msec versus mm and tenths of a second. The aim of measurement here is to establish the wave packet as the information carrier at the mesoscopic level in brain dynamics, comparable to the role of the action potential as the information carrier at the microscopic level in neuron dynamics.

In this paper, based on the two-compartment unidirectionally coupled thalamocortical model network, we investigated the transition dynamics of epileptic seizures, by considering the inhibitory coupling strength from cortical inhibitory interneuronal (IN) population to excitatory pyramidal (PY) neuronal population as the key bifurcation parameter. The results show that in the single compartment thalamocortical model, inner-compartment inhibitory functions of IN can make the system transit from the absence seizures to the tonic oscillations. In the case of two-compartment coupled thalamocortical model network, the inter-compartment inhibitory coupling functions from the first compartment can drive the second compartment to more easily initiate the absence and tonic seizures at the lower inhibitory coupling strengths, respectively. Also, the driven functions can make the amplitudes of these seizures vary irregularly. Detailed investigations reveal that along with the various state transitions, the system consecutively undergoes Hopf bifurcations, fold of cycles bifurcations and torus bifurcations, respectively. In particular, the reinforcing inter-compartment inhibitory coupling function can induce the chaotic dynamics. We highlight the unidirectional coupling functions between two compartments which might give new insights into the propagation and evolution dynamics of epileptic seizures.

Introducing the memcapacitor into the Cellular Neural Network (CNN), the Memcapacitor-Cellular Neural Network (MC-CNN) model with infinitely many equilibrium points is constructed. A series of dynamical behaviors of the MC-CNN are investigated by various nonlinear system analysis means. It is shown that the system has a large maximum Lyapunov exponent in a specific parameter range. And with the variation of parameters, the system is able to produce many different phase trajectories of the attractor. Multistability is also found in the system. The pseudo-randomness of the MC-CNN is calculated by Spectral Entropy (SE) complexity algorithm. The final hardware results proves the physical realizability of the system. The MC-CNN model is intended to provide guidance for neural networks and cryptographic strategies based on the memcapacitor.

In this paper, a new discrete chaotic map is constructed by introducing a discrete memristor in two-dimensional generalized square maps to enhance its chaotic performance. First, the fixed points of the new maps are analyzed, and the effects of different parameters on the system performance are investigated by bifurcation diagrams, Lyapunov exponential spectra and phase diagrams. Second, the fixed points of the new maps are analyzed, and the effects of different parameters on the system performance are investigated by bifurcation diagrams, Lyapunov exponential spectra and phase diagrams. The distinctive characteristic of a discrete system is the coexistence of various types of attractors, and there is coexistence of hyperchaos and cycles in the present maps. It is worth mentioning that symmetric chaotic attractors with different positive and negative parameters are found during the study. In addition, the phenomenon of state transition between chaos and cycles is also found. Finally, the discrete maps are designed and implemented using a DSP platform. The results of the study provide a reference for the application of discrete amnesic chaotic maps.

Sensing and perceiving involve enormous numbers of widely distributed dendritic and action potentials in cortex, before, during and after stimulus arrival but with differing spatiotemporal patterns. Stimulus-activated receptors drive cortical neurons directly (olfactory) or indirectly through thalamocortical relays. The driven activity induces hemisphere-wide, self-organized patterns of neural activity called wave packets. Three levels of brain function are hypothesized to mediate transition from sensation and perception. Microscopic activity expressed by action potentials is sensory. Macroscopic activity of the whole forebrain expressed by behavior is perceptual. Mesoscopic activity bridges the gap by the formation of wave packets. They form when sensory input destabilizes the primary receiving areas by local state transitions. The sensory-driven action potentials condense into mesoscopic wave packets like molecules forming raindrops from vapor. The condensation disks sustain 2D spatial patterns of phase and amplitude of carrier waves in the beta and gamma EEG. The AM patterns correlate not with features but with the context and value of sensory stimuli for the subjects, in a word, their meaning. The wave packets from all sensory areas are broadly transmitted through the forebrain. They induce the formation of macroscopic patterns that coalesce like scintillating pools over much and perhaps all of each hemisphere. The prediction is made for clinical testing that wave packets are precursor to states of awareness. They are not by themselves accessible to experience, as may be the macroscopic states initiated by global state transitions.