Neural Oscillator Model Research Articles

Bifurcation analysis of a two-neuron central pattern generator model for both oscillatory and convergent neuronal activities.

The neural oscillator model proposed by Matsuoka is a piecewise affine system that exhibits distinctive periodic solutions. Although such typical oscillation patterns have been widely studied, little is understood about the dynamics of convergence to certain fixed points and bifurcations between the periodic orbits and fixed points in this model. We performed fixed point analysis on a two-neuron version of the Matsuoka oscillator model, the result of which explains the mechanism of oscillation and the discontinuity-induced bifurcations such as subcritical/supercritical Hopf-like, homoclinic-like and grazing bifurcations. Furthermore, it provided theoretical predictions concerning a logarithmic oscillation-period scaling law and noise-induced oscillations observed around those bifurcations. These results are expected to underpin further investigations into oscillatory and transient neuronal activities concerning central pattern generators.

A neuromuscular model of human locomotion combines spinal reflex circuits with voluntary movements

Existing models of human walking use low-level reflexes or neural oscillators to generate movement. While appropriate to generate the stable, rhythmic movement patterns of steady-state walking, these models lack the ability to change their movement patterns or spontaneously generate new movements in the specific, goal-directed way characteristic of voluntary movements. Here we present a neuromuscular model of human locomotion that bridges this gap and combines the ability to execute goal directed movements with the generation of stable, rhythmic movement patterns that are required for robust locomotion. The model represents goals for voluntary movements of the swing leg on the task level of swing leg joint kinematics. Smooth movements plans towards the goal configuration are generated on the task level and transformed into descending motor commands that execute the planned movements, using internal models. The movement goals and plans are updated in real time based on sensory feedback and task constraints. On the spinal level, the descending commands during the swing phase are integrated with a generic stretch reflex for each muscle. Stance leg control solely relies on dedicated spinal reflex pathways. Spinal reflexes stimulate Hill-type muscles that actuate a biomechanical model with eight internal joints and six free-body degrees of freedom. The model is able to generate voluntary, goal-directed reaching movements with the swing leg and combine multiple movements in a rhythmic sequence. During walking, the swing leg is moved in a goal-directed manner to a target that is updated in real-time based on sensory feedback to maintain upright balance, while the stance leg is stabilized by low-level reflexes and a behavioral organization switching between swing and stance control for each leg. With this combination of reflex-based stance leg and voluntary, goal-directed control of the swing leg, the model controller generates rhythmic, stable walking patterns in which the swing leg movement can be flexibly updated in real-time to step over or around obstacles.

Switch Elements with S-Shaped Current-Voltage Characteristic in Models of Neural Oscillators

In this paper, we present circuit solutions based on a switch element with the S-type I–V characteristic implemented using the classic FitzHugh–Nagumo and FitzHugh–Rinzel models. Using the proposed simplified electrical circuits allows the modeling of the integrate-and-fire neuron and burst oscillation modes with the emulation of the mammalian cold receptor patterns. The circuits were studied using the experimental I–V characteristic of an NbO2 switch with a stable section of negative differential resistance (NDR) and a VO2 switch with an unstable NDR, considering the temperature dependences of the threshold characteristics. The results are relevant for modern neuroelectronics and have practical significance for the introduction of the neurodynamic models in circuit design and the brain–machine interface. The proposed systems of differential equations with the piecewise linear approximation of the S-type I–V characteristic may be of scientific interest for further analytical and numerical research and development of neural networks with artificial intelligence.

Layered neural-based locomotion for biped robot movement with carrying dynamic payload

This paper proposes layered neural based locomotion with a hierarchical learning process. Central pattern generation (CPG) in a higher layer generates an analog signal to the lower layer which is Motor Neurons Pools. In a lower layer, motor neuron generates the angular velocity of the joint. Central pattern generation is built based on neural oscillator model in the spinal cord. It responds to the pattern of locomotion model. Then, the inner state of a motor neuron is developed based on muscle activity in the human musculoskeletal model. Furthermore, the motor neurons pools (MNs) are integrated with sensory neurons (SNs) that send the internal feedback of the robot. There are two steps of the learning process: 1) optimizing the structure of CPG for generating appropriate behavior without considering the feedback information 2) optimizing the integration between MNs and SNs for generating adaptive behavior toward internal disturbance. The proposed model has been implemented in a simulated humanoid robot with carrying different weight of payloads. The robot behavior changes for stabilizing the robot posture.

The Complex Behaviour of a Simple Neural Oscillator Model in the Human Cortex.

The brain is a complex organ responsible for memory storage and reasoning; however, the mechanisms underlying these processes remain unknown. This paper forms a contribution to a lot of theoretical studies devoted to regular or chaotic oscillations of interconnected neurons assuming that the smallest information unit in the brain is not a neuron but, instead, a coupling of inhibitory and excitatory neurons forming a simple oscillator. Several coefficients of variation for peak intervals and correlation coefficients for peak interval histograms are evaluated and the sensitivity of such oscillator units is tested to changes in initial membrane potentials, interconnection signal delays, and changes in synaptic weights based on known histologically verified neuron couplings. Results present only a low dependence of oscillation patterns to changes in initial membrane potentials or interconnection signal delays in comparison to a strong sensitivity to changes in synaptic weights showing the stability and robustness of encoded oscillating patterns to signal outages or remoteness of interconnected neurons. Presented simulations prove that the selected neuronal couplings are able to produce a variety of different behavioural patterns, with periodicity ranging from milliseconds to thousands of milliseconds between the spikes. Many detected different intrinsic frequencies then support the idea of possibly large informational capacity of such memory units.

Modulation of Cortical Oscillations by Low-Frequency Direct Cortical Stimulation Is State-Dependent.

Cortical oscillations play a fundamental role in organizing large-scale functional brain networks. Noninvasive brain stimulation with temporally patterned waveforms such as repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS) have been proposed to modulate these oscillations. Thus, these stimulation modalities represent promising new approaches for the treatment of psychiatric illnesses in which these oscillations are impaired. However, the mechanism by which periodic brain stimulation alters endogenous oscillation dynamics is debated and appears to depend on brain state. Here, we demonstrate with a static model and a neural oscillator model that recurrent excitation in the thalamo-cortical circuit, together with recruitment of cortico-cortical connections, can explain the enhancement of oscillations by brain stimulation as a function of brain state. We then performed concurrent invasive recording and stimulation of the human cortical surface to elucidate the response of cortical oscillations to periodic stimulation and support the findings from the computational models. We found that (1) stimulation enhanced the targeted oscillation power, (2) this enhancement outlasted stimulation, and (3) the effect of stimulation depended on behavioral state. Together, our results show successful target engagement of oscillations by periodic brain stimulation and highlight the role of nonlinear interaction between endogenous network oscillations and stimulation. These mechanistic insights will contribute to the design of adaptive, more targeted stimulation paradigms.

A unified neural oscillator model for various rhythmic locomotions of snake-like robot

This paper contributes to the understanding and implementation of different types of locomotion in a snake-like robot by using a proposed unified neural oscillator model as central pattern generator (CPG). A neural oscillator network is suggested so that several rhythmic movements can be generated in order to mimic the actual snake movements on land. The unified coupled neural oscillators in the network provide the desired orientation and displacement for the snake-like robot and they are applied to the different types of snake locomotion by just altering some of the parameters proposed in the paper. The design of snake-like robot, consisting of a series of wheeled links (links with active wheels) connected with each other using the passive prismatic and revolute joints, is also suggested in the paper. The passive prismatic joints facilitate the change of lengths of wheel-less links and in this way the robot can be elongated as well as shortened. In this paper the serpentine, rectilinear, and concertina types of actual snake locomotion are realized, through simulation studies, by using the unified neural oscillator model proposed for the snake-like robots.

Task-Oriented Parameter Tuning Based on Priority Condition for Biologically Inspired Robot Application

This work gives a biologically inspired control scheme for controlling a robotic system. Novel adaptive behaviors are observed from humans or animals even in unexpected disturbances or environment changes. This is why they have neural oscillator networks in the spinal cord to yield rhythmic-motor primitives robustly under a changing task. Hence, this work focuses on rhythmic arm movements that can be accomplished in terms of employing a control approach based on an artificial neural oscillator model. The main challenge is to determine various parameters for applying a neural feedback to robotic systems with performing a desired behavior and self-maintaining the entrainment effect. Hence, this work proposes a task-oriented parameter tuning algorithm based on the simulated annealing (SA). This work also illustrates how to technically implement the proposed control scheme exploiting a virtual force and neural feedback. With parameters tuned, it is verified in simulations that a 3-DOF planar robotic arm traces a given trajectory precisely, adapting to uneven external disturbances.

Mean field limit for disordered diffusions with singular interactions

Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf{R} ^{m}$ in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice $\mathbf{Z} ^{d}$, and the interaction between two diffusions is attenuated by a spatial weight that depends on their positions. For a general class of singular weights (including the case already considered in the physical literature when interactions obey to a power-law of parameter $0<\alpha<d$), we address the convergence as $N\to\infty$ of the empirical measure of the diffusions to the solution of a deterministic McKean–Vlasov equation and prove well-posedness of this equation, even in the degenerate case without noise. We provide also precise estimates of the speed of this convergence, in terms of an appropriate weighted Wasserstein distance, exhibiting in particular nontrivial fluctuations in the power-law case when $\frac{d}{2}\leq\alpha<d$. Our framework covers the case of polynomially bounded monotone dynamics that are especially encountered in the main models of neural oscillators.

Self-organization of a recurrent network under ongoing synaptic plasticity

We investigated the organization of a recurrent network under ongoing synaptic plasticity using a model of neural oscillators coupled by dynamic synapses. In this model, the coupling weights changed dynamically, depending on the timing between the oscillators. We determined the phase coupling function of the oscillator model, Γ(ϕ), using conductance-based neuron models. Furthermore, we examined the effects of the Fourier zero mode of Γ(ϕ), which has a critical role in the case of spike-time-dependent plasticity-organized recurrent networks. Heterogeneous layered clusters with different frequencies emerged from homogeneous populations as the Fourier zero mode increased. Our findings may provide new insights into the self-assembly mechanisms of neural networks related to synaptic plasticity.

20218 神経振動子モデルを用いた歩行アシスト機器の制御

20218 神経振動子モデルを用いた歩行アシスト機器の制御

An artificial neural network model for serial speech production and speech error simulation

This paper presents serial speech gesture encoding and recall extension to the Neural Oscillator Model Speech Timing and Rhythm (NOMSTR), previously used to simulate prosodic and syllable timing (Rusaw 2010, 2013), and describes how it can be used to simulate speech errors and speech error patterns. This model uses NOMSTR to provide the phonological context vector which drives its serial recall, activating a series of gesture output nodes. Besides the prosodic context signal, the gesture output nodes have two other sources of input: (1) Nuclear gestures nodes provide excitatory input to the nodes required to produce the onset and coda gestures they share a syllable with; this mechanism is the ANN instantiation of the nucleus-centered syllable model. (2) Second, nuclear gesture nodes receive excitatory input from NOMSTR’s syllable-level thresholded node, which ties the timing of the gestures in a syllable to the time at which the syllable occurs in the phonological output. This extended version of NOMSTR is shown to able to simulate aspects of speech error behavior which other models have been unable to explain, such as C/V error (O-C/N) asymmetry, and error dependence (Rusaw and Cole 2009). [Work supported by NSF and NIH.]

Modeling of Fish Adaptive Behaviors in Unsteady Flows

Fish can swim swiftly in complicated flow environments, which conceives inspirations for man-made underwater vehicles. This paper concentrates on observation and modeling of fish adaptive behaviors in unsteady flows. A good representative of bony fish, crucian, is taken as the experimental specimen for investigating biological adaptation with response to alteration of surrounding flow patterns. Difference of swimming parameters is confirmed by recorded samples within several flow patterns. Furthermore, a bio-inspired gait model is constructed to stimulate fish adaptive behaviors, since the traditional model is hardly suitable. The model is inspired and supported by biological neural oscillators. By using the developed neural oscillator model, not only certain rhythmic motions under a steady flow pattern can be generated, but also behavioral transitions between multiple different patterns within unsteady flows come true. Experimental results validate the effectiveness of the developed neural model in continuously and smoothly regulating fish propulsive patterns within unsteady flows.

Phase-Amplitude Descriptions of Neural Oscillator Models

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris–Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.

Color Image Segmentation Based on Dynamic Model and Power Spectrum

In this paper, the locally coupled neural oscillator model and power spectrum are introduced to solve the color image segmentation problem. Firstly the single neuron oscillator model is developed, the model parameter is set so as to create limit circle simulating the activity of neuron. Then the locally coupled network model is developed, taking R, G, Bas external input separately, the network output three dynamic orbits representing R, G, B for each image point. Lastly, the power spectrum of the orbits is calculated for each image point, the color image is segmented using the calculated power spectrum. The performance is comparable to the results from other segmentation methods.

Quantum-like model of behavioral response computation using neural oscillators

In this paper we propose the use of neural interference as the origin of quantum-like effects in the brain. We do so by using a neural oscillator model consistent with neurophysiological data. The model used was shown elsewhere to reproduce well the predictions of behavioral stimulus-response theory. The quantum-like effects are brought about by the spreading activation of incompatible oscillators, leading to an interference-like effect mediated by inhibitory and excitatory synapses.

Phasic bursting pattern of postural responses may reflect internal dynamics: Simulation of trunk reflexes with a neural oscillator model

Postural responses are usually investigated as reflexes. Several trials are averaged, and trial-to-trial variations are interpreted as noise. Several studies providing single-trial data plots revealed oscillations that may be cancelled out in averaged time series. Variations between single trials may also be interpreted as a consequence of changed dynamic properties of the neural circuitries. Therefore, we propose a Matsuoka oscillator model to describe single-trial postural responses to external perturbations. The applicability of the model was demonstrated by a comparison between simulations and experimental electromyographic (EMG) data. Vertical force perturbations of durations 0.4s and 0.2s were applied via a handle to 10 subjects. Handle force was used as model input, and EMG data from the external oblique muscles was compared with simulation output. Model coefficients were optimized by a least-squares algorithm. The optimization produced a good similarity between simulation and experimental data with determination coefficients of r2=0.7 and greater. Furthermore, as a model validation, the model coefficients were used to predict other perturbation trials with similarities between predictions and respective EMG data of about r2=0.45, which was in the range of trial-to-trial EMG variability. The observed oscillations are assumed to originate from the central nervous system with changes in the neural circuitries between trials. Hence, the oscillations in single trial responses which are usually regarded as noise might be generated by the dynamics of a neural oscillator.

Phase-oscillator computations as neural models of stimulus–response conditioning and response selection

The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto’s equations. In this article, we build such neural-oscillator models, partly based on neurophysiological evidence, to represent approximately the learning behavior predicted and confirmed in three experiments by well-known stochastic learning models of behavioral stimulus–response theory. We use three Kuramoto oscillators to model a continuum of responses, and we provide detailed numerical simulations and analysis of the three-oscillator Kuramoto problem, including an analysis of the stability points for different coupling conditions. We show that the oscillator simulation data are well-matched to the behavioral data of the three experiments.

Force-feedback interaction with a neural oscillator model: for shared human-robot control of a virtual percussion instrument

A study on force-feedback interaction with a model of a neural oscillator provides insight into enhanced human-robot interactions for controlling musical sound. We provide differential equations and discrete-time computable equations for the core oscillator model developed by Edward Large for simulating rhythm perception. Using a mechanical analog parameterization, we derive a force-feedback model structure that enables a human to share control of a virtual percussion instrument with a "robotic" neural oscillator. A formal human subject test indicated that strong coupling (STRNG) between the force-feedback device and the neural oscillator provided subjects with the best control. Overall, the human subjects predominantly found the interaction to be "enjoyable" and "fun" or "entertaining." However, there were indications that some subjects preferred a medium-strength coupling (MED), presumably because they were unaccustomed to such strong force-feedback interaction with an external agent. With related models, test subjects performed better when they could synchronize their input in phase with a dominant sensory feedback modality. In contrast, subjects tended to perform worse when an optimal strategy was to move the force-feedback device with a 90° phase lag. Our results suggest an extension of dynamic pattern theory to force-feedback tasks. In closing, we provide an overview of how a similar force-feedback scenario could be used in a more complex musical robotics setting.

Inhibition of Oscillation in a Neural Oscillator Model for Sound Therapy of Tinnitus

Perception of continuous or intermittent sounds ringing in the ears without any external source is referred to as tinnitus. For the management of tinnitus one of the most effective approaches is sound therapy. Previously, we demonstrated a conceptual and computational plastic neural oscillator model for the mechanisms of tinnitus generation and the clinical effects of sound therapy on tinnitus. The proposed model has a stable oscillatory state and a stable equilibrium (non-oscillatory) state. It can be hypothesized that the oscillation state corresponds to the generation of tinnitus and the equilibrium state corresponds to the state in which the tinnitus is inhibited. Through numerical simulations of this model it was found that the oscillation can be inhibited by supplying band-pass noise (BN) stimuli, which clinically has been used as a stimulus for treatment of tinnitus (i.e., sound therapy). The current paper describes the inhibition of the oscillation by yet two different types of noise stimuli: Gaussian white noise (GWN) and additive uniform noise (AUN). This investigation shows that only smaller RMS value of GWN input could inhibit the oscillation. When larger RMS values of GWN were employed the inhibition of oscillation was not frequent. It was observed that AUN can inhibit the oscillation with higher possibility than GWN or BN. It is an interesting result although it does not directly suggest that AUN is better than GWN or BN in clinic.