Dynamic Recurrent Network Research Articles

Dynamic Recurrent Wavelet Neural Network Observer Based Tracking Control for a Class of Uncertain Nonaffine Systems

In this paper, a dynamic recurrent wavelet neural network observer and tracking control strategy is presented for a class of uncertain, nonaffine systems. In proposed scheme a dynamic recurrent wavelet network is used to design a nonlinear observer .Adaptation laws are developed for the online tuning of wavelet parameters. Based on the estimated states, a state feedback control law is derived to achieve the desired tracking performance. The stability of closed loop system and ultimate upper boundedness all closed loop signals is proven in Lyapunov sense. Effectiveness of proposed scheme is demonstrated through numerical simulation.

Dynamic Recurrent Wavelet Neural Network Observer Based Tracking Control for a Class of Uncertain Nonaffine Systems

In this paper, a dynamic recurrent wavelet neural network observer and tracking control strategy is presented for a class of uncertain, nonaffine systems. In proposed scheme a dynamic recurrent wavelet network is used to design a nonlinear observer .Adaptation laws are developed for the online tuning of wavelet parameters. Based on the estimated states, a state feedback control law is derived to achieve the desired tracking performance. The stability of closed loop system and ultimate upper boundedness all closed loop signals is proven in Lyapunov sense. Effectiveness of proposed scheme is demonstrated through numerical simulation.

Complex dynamics in recurrent cortical networks based on spatially realistic connectivities

Most studies on the dynamics of recurrent cortical networks are either based on purely random wiring or neighborhood couplings. Neuronal cortical connectivity, however, shows a complex spatial pattern composed of local and remote patchy connections. We ask to what extent such geometric traits influence the “idle” dynamics of two-dimensional (2d) cortical network models composed of conductance-based integrate-and-fire (iaf) neurons. In contrast to the typical 1 mm2 used in most studies, we employ an enlarged spatial set-up of 25 mm2 to provide for long-range connections. Our models range from purely random to distance-dependent connectivities including patchy projections, i.e., spatially clustered synapses. Analyzing the characteristic measures for synchronicity and regularity in neuronal spiking, we explore and compare the phase spaces and activity patterns of our simulation results. Depending on the input parameters, different dynamical states appear, similar to the known synchronous regular “SR” or asynchronous irregular “AI” firing in random networks. Our structured networks, however, exhibit shifted and sharper transitions, as well as more complex activity patterns. Distance-dependent connectivity structures induce a spatio-temporal spread of activity, e.g., propagating waves, that random networks cannot account for. Spatially and temporally restricted activity injections reveal that a high amount of local coupling induces rather unstable AI dynamics. We find that the amount of local versus long-range connections is an important parameter, whereas the structurally advantageous wiring cost optimization of patchy networks has little bearing on the phase space.

The relationship between cortical network structure and the corresponding state space dynamics

Most studies on the dynamics of recurrent cortical networks are either based on purely random wiring or neighborhood couplings [1-3]. Neuronal wiring in the cortex, however, shows a complex spatial pattern composed of local and long-range patchy connections, i.e., spatially clustered synapses [4,5]. We ask to what extent such geometric traits influence the 'idle' dynamics of cortical network models. Assuming an enlarged spatial scale we consider distinct network architectures, ranging from purely random or purely locally coupled neurons to distance dependent connectivities that also include patchy projections. Approximately 50000 neurons are spatially embedded in a 2D sheet of cortex with a side length of five millimeters in order to account for remotely established synapses. Neurons are implemented as conductance based integrate-and-fire neurons with distance-dependent synaptic delays. Network dynamics are simulated with NEST/PyNN [6]. Analyzing the characteristic measures describing spiking neuronal networks (e.g. the correlation coefficient or the coefficient of variation), we explore and compare the phase spaces and activity patterns of our simulation results. As expected from random networks, different dynamical states (e.g. synchronous regular 'SR' or asynchronous irregular 'AI' firing) occur in dependence of the input rate and the relation between exc. and inh. synaptic strengths [1-3]. Non-random networks, however, exhibit higher firing rates, sharper transitions, as well as various types of complex network activities. For example, the amount of local connections clearly influences the boundaries at which the network switches from high (SR) to low (AI) activity. Distance-dependent connectivity structures induce 'new' raster plots, e.g., oblique stripes or spiral structures representing planar and spherical wave propagation. To better describe such activity patterns we computed a delay-dependent correlation coefficient. Such spike patterns indicate a spatio-temporal spread of activity that random networks cannot account for. Furthermore, to determine stability and signal propagation properties, we applied spatially restricted activity injections. Depending on the network architecture, the dynamics may change from AI to SR or wave-like activity, and then switch back or not. We conclude that (the amount of) local distance-dependent connections is an important structural feature of cortical networks since it induces rather complex activity patterns compared to random connectivities. However, we found no clear differences in the dynamics of networks with randomly distributed compared to spatially clustered long-range projections. Further analysis is needed to explore the functional aspects of patchy projection patterns.

Dynamics of Networks of Excitatory and Inhibitory Neurons in Response to Time-Dependent Inputs

We investigate the dynamics of recurrent networks of excitatory (E) and inhibitory (I) neurons in the presence of time-dependent inputs. The dynamics is characterized by the network dynamical transfer function, i.e., how the population firing rate is modulated by sinusoidal inputs at arbitrary frequencies. Two types of networks are studied and compared: (i) a Wilson–Cowan type firing rate model; and (ii) a fully connected network of leaky integrate-and-fire (LIF) neurons, in a strong noise regime. We first characterize the region of stability of the “asynchronous state” (a state in which population activity is constant in time when external inputs are constant) in the space of parameters characterizing the connectivity of the network. We then systematically characterize the qualitative behaviors of the dynamical transfer function, as a function of the connectivity. We find that the transfer function can be either low-pass, or with a single or double resonance, depending on the connection strengths and synaptic time constants. Resonances appear when the system is close to Hopf bifurcations, that can be induced by two separate mechanisms: the I–I connectivity and the E–I connectivity. Double resonances can appear when excitatory delays are larger than inhibitory delays, due to the fact that two distinct instabilities exist with a finite gap between the corresponding frequencies. In networks of LIF neurons, changes in external inputs and external noise are shown to be able to change qualitatively the network transfer function. Firing rate models are shown to exhibit the same diversity of transfer functions as the LIF network, provided delays are present. They can also exhibit input-dependent changes of the transfer function, provided a suitable static non-linearity is incorporated.

Decorrelation of low-frequency neural activity by inhibitory feedback

To correctly judge the functional role of cooperative neural activity it is essential to understand how neural correlations are determined by the structure and dynamics of neural networks. Shared presynaptic input is one of the major sources of correlated synaptic activity in such systems. In the asynchronous state of recurrent neural network models, however, spike correlations are considerably smaller than what one would expect based on the amount of shared presynaptic sources [1,2]. A similar lack of correlations in the spiking activity of neighbouring cortical neurons has been observed experimentally [3]. Recently, it has been pointed out that shared-input correlations can be actively suppressed by the dynamics of recurrent networks [4]. Here, we show that both in networks with purely inhibitory coupling (Fig. ​(Fig.1A)1A) and in those with mixed excitatory-inhibitory coupling (Fig. ​(Fig.1B)1B) this active decorrelation affects mainly the activity at low frequencies (<20 Hz). High-frequency activity, in contrast, is rather unaffected. Simulations rule out that this phenomenon is the result of refractoriness. By means of a simple linear population-rate model we demonstrate that the effect is essentially explained by inhibitory feedback. Figure 1 Population-rate power spectra for an inhibitory (A) and a balanced recurrent network (B) of leaky integrate-and-fire model neurons (black curves). Grey curves represent population-rate spectra of ensembles of unconnected neurons receiving stationary Poisson ...

Population Models of Temporal Differentiation

Temporal derivatives are computed by a wide variety of neural circuits, but the problem of performing this computation accurately has received little theoretical study. Here we systematically compare the performance of diverse networks that calculate derivatives using cell-intrinsic adaptation and synaptic depression dynamics, feedforward network dynamics, and recurrent network dynamics. Examples of each type of network are compared by quantifying the errors they introduce into the calculation and their rejection of high-frequency input noise. This comparison is based on both analytical methods and numerical simulations with spiking leaky-integrate-and-fire (LIF) neurons. Both adapting and feedforward-network circuits provide good performance for signals with frequency bands that are well matched to the time constants of postsynaptic current decay and adaptation, respectively. The synaptic depression circuit performs similarly to the adaptation circuit, although strictly speaking, precisely linear differentiation based on synaptic depression is not possible, because depression scales synaptic weights multiplicatively. Feedback circuits introduce greater errors than functionally equivalent feedforward circuits, but they have the useful property that their dynamics are determined by feedback strength. For this reason, these circuits are better suited for calculating the derivatives of signals that evolve on timescales outside the range of membrane dynamics and, possibly, for providing the wide range of timescales needed for precise fractional-order differentiation.

Structural motifs and correlation dynamics in networks of spiking neurons

Event Abstract Back to Event Structural motifs and correlation dynamics in networks of spiking neurons Volker Pernice1*, Benjamin Staude1 and Stefan Rotter1 1 Albert-Ludwig University, Bernstein Center Freiburg & Faculty of Biology, Germany The dynamics of random recurrent networks has been analyzed in detail, but the influence of non-random connectivity patterns [1] on activity dynamics is not well understood. Here we study the effect of certain structural motifs on pairwise correlations in spiking networks of excitatory and inhibitory neurons in a balanced asynchronous-irregular state. For analytical tractability, spike trains are conceived as linearly interacting stochastic point processes. In this case, firing rates and correlation functions are fully determined by the matrix of linear response kernels. Simple analytic expressions have been derived in [2]. We find that the matrix of integrated cross-covariance functions can be written as a power series of the underlying network’s connectivity matrix. In terms of network structure, higher matrix powers of this series expansion can be interpreted as contributions of motifs of increasing complexity. Generally, such higher order motifs can strongly affect correlations. Their impact can be estimated from the spectral radius of the connectivity matrix. Using numerical simulations, we demonstrate that not only differences in average in-degree and common input but also in higher order motif distributions can lead to dramatic effects regarding pairwise correlations.To illustrate the influence of network structure in more detail, we study connectivity matrices with certain symmetry properties. Specifically we focus on distance dependent connectivity profiles. The distance dependence of correlations can then be determined from the connectivity profile, and the influence of higher order contributions can be understood analytically.

Beyond linear perturbation theory: the instantaneous response of the integrate-and-fire model

Event Abstract Back to Event Beyond linear perturbation theory: the instantaneous response of the integrate-and-fire model Moritz Helias1*, Moritz Deger2, Stefan Rotter2 and Markus Diesmann1 1 RIKEN Brain Science Institute, Japan 2 Bernstein Center for Computational Neuroscience, Germany The integrate-and-fire neuron model with exponential postsynaptic potentials is widely used in analytical work and in simulation studies of neural networks alike. For Gaussian white noise input currents, the membrane potential distribution is known exactly [1]. The linear response properties of the model have successfully been calculated and applied to the dynamics of recurrent networks in this diffusion limit [2]. However, the diffusion approximation assumes the effect of each synapse on the membrane potential to be infinitesimally small. Here we present a novel hybrid theory that takes finite synaptic weights into account. We show, that this considerably alters the absorbing boundary condition at the threshold: the probability density increases just below threshold. As a result, the response of the neuron to a fast transient input is enhanced much in the same way as found for the case of synaptic filtering [3]. However, in contrast to this earlier work relying on linear perturbation theory [4], we quantify to all orders an instantaneous response that is asymmetric for excitatory and inhibitory transients and exhibits a non-linear dependence on positive perturbation amplitudes. Furthermore we demonstrate that in the pooled response of two neuronal populations to antisymmetric transients the linear components exactly cancel. In this scenario the macroscopic network dynamics is dominated by the instantaneous non-linear components of the response. These results suggest that the linear response approach neglects important features of the rectifying nature of threshold units with finite jumps even for small perturbations. We provide an analytical framework to go beyond [5]. Partially funded by BMBF Grant 01GQ0420 to BCCN Freiburg, EU Grant 15879 (FACETS), DIP F1.2, Helmholtz Alliance on Systems Biology, and Next-Generation Supercomputer Project of MEXT.

Reliable Recall of Spontaneous Activity Patterns in Cortical Networks

Irregular ongoing activity in cortical networks is often modeled as arising from recurrent connectivity. Yet it remains unclear to what extent its presence corrupts sensory signal transmission and network computational capabilities. In a recurrent cortical-like network, we have determined the activity patterns that are better transmitted and self-sustained by the network. We show that reproducible spiking and subthreshold dynamics can be triggered if the statistics of the imposed external drive are consistent with patterns previously seen in the ongoing activity. A subset of neurons in the network, constrained to replay temporal pattern segments extracted from the recorded ongoing activity of the same network, reliably drives the remaining, free-running neurons to call the rest of the pattern. Comparison with surrogate Poisson patterns indicates that the efficiency of the recall and completion process depends on the similarity between the statistical properties of the input with previous ongoing activity The reliability of evoked dynamics in recurrent networks is thus dependent on the stimulus used, and we propose that the similarity between spontaneous and evoked activity in sensory cortical areas could be a signature of efficient transmission and propagation across cortical networks.

Implications of synaptic biophysics for recurrent network dynamics and active memory

In cortical networks, synaptic excitation is mediated by AMPA- and NMDA-type receptors. NMDA differ from AMPA synaptic potentials with regard to peak current, time course, and a strong voltage-dependent nonlinearity. Here we illustrate based on empirical and computational findings that these specific biophysical properties may have profound implications for the dynamics of cortical networks, and via dynamics on cognitive functions like active memory. The discussion will be led along a minimal set of neural equations introduced to capture the essential dynamics of the various phenomena described. NMDA currents could establish cortical bistability and may provide the relatively constant synaptic drive needed to robustly maintain enhanced levels of activity during working memory epochs, freeing fast AMPA currents for other computational purposes. Perhaps more importantly, variations in NMDA synaptic input-due to their biophysical particularities-control the dynamical regime within which single neurons and networks reside. By provoking bursting, chaotic irregularity, and coherent oscillations their major effect may be on the temporal pattern of spiking activity, rather than on average firing rate. During active memory, neurons may thus be pushed into a spiking regime that harbors complex temporal structure, potentially optimal for the encoding and processing of temporal sequence information. These observations provide a qualitatively different view on the role of synaptic excitation in neocortical dynamics than entailed by many more abstract models. In this sense, this article is a plead for taking the specific biophysics of real neurons and synapses seriously when trying to account for the neurobiology of cognition.

Spatial organization of evoked neuronal dynamics in 2D recurrent networks, with or without structured stimulation

Neuronal dynamics in the awake mammalian cortex are known to display highly irregular spiking activity and asynchronous firing patterns at the population level (AI regime). Many computational models have proposed simplified benchmarks to investigate information propagation in such regimes [1]. However, to allow explicit analytical analysis, most of them assume random connectivity within the network, no propagation delays and unstructured Poisson external input [2]. In particular, for AI regimes, these models do not exhibit any substantial spatial correlations [3]. In contrast, in biological V1, it has been observed that the large-scale dynamics produced by ongoing reverberation correspond to spatially structured activity maps characterized by distance-dependent correlations [4,5]. A realistic model of sensory neocortex should thus take into account the presence of intrinsic spatial correlation in order to study how this may interfere with structured correlation evoked by the sensory drive.

Finite synaptic potentials cause a non-linear instantaneous response of the integrate-and-fire model

The integrate-and-fire neuron model with exponential postsynaptic potentials is widely used in analytical work and in simulation studies of neural networks alike. For Gaussian white noise input currents, the membrane potential distribution is described by a population density approach [1]. The linear response properties of the model have successfully been calculated and applied to the dynamics of recurrent networks in this diffusion limit [2]. However, the diffusion approximation assumes the effect of each synapse on the membrane potential to be infinitesimally small. Here, we go beyond this limit and allow for finite synaptic weights. We show that this considerably alters the absorbing boundary condition at the threshold. In contrast to the diffusion limit, the probability density goes to zero on the scale of the amplitude of a postsynaptic potential (Figure 1). We give an analytic approximafrom Eighteenth Annual Computational Neuroscience Meeting: CNS*2009 Berlin, Germany. 18–23 July 2009

Correlations in spiking neuronal networks with distance dependent connections

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.

A Recurrent Network of Macrocolumnar Models for Face Recognition

Event Abstract Back to Event A Recurrent Network of Macrocolumnar Models for Face Recognition Yasuomi Sato1, 2*, Jenia Jitsev1, 3, Philipp Wolfrum1, Christoph Von Der Malsburg1 and Takashi Morie2 1 Frankfurt Institute for Advanced Studies, Germany 2 Kyushu Institute of Technology, Japan 3 Goethe University, Germany Invariance is a key mechanism to understand in-depth visual object recognition in a human brain. Invariant object recognition is achieved by correct matching of a sensory input image to its most suitable representation stored in memory. The required information about one single object, for example, a position and a shape, are initially uncertain under a realistic visual condition The most likely shape and positional information must be specified or detected selectively to integrate both the information into one entire identity. “What”-information about a particular object is identified by finding correct correspondence of an input image to its related image representation, to be more precise, by finding a set of points, which can extract Gabor features for the input image and can then be identified as the same points extracting the similar feature from the stored image. In addition, the “where”-information about the relevant object should be detected, binding it to the object information. We have to propose a neurally plausible mechanism on focal or spatial attention when attention is oriented to a particular locus in the environment.In this work, we are aiming at developing an artificial visual object recognition system being capable of focal attention by making effective use of an invariant recognition. The system depends on finding a best balance of Gabor feature similarities and topological constraints of feature extraction sets. It is based on a global recurrent hierarchical switchyard system of a macrocolumnar cortical model, setting several intermediate layers between an input layer and the higher model layer. The recognition system possesses a crucial function for the correspondence finding, which can save the Gabor feature quality of one intermediate layer to the next intermediate layer as decreasing the number of Gabor feature representations in higher and higher intermediate layers. It facilitates input information flow in the bottom-up to match the most suitable representation in the model layer, at the same time, detecting a position of the object on the input via focal attention in the top-down flow. The dynamical recurrent macrocolumnar network has an ability for integrating shape- and position-information of a particular a particular object even though such information are uncertain.Acknowledgements: This work was supported by the European Commission-funded project, “Neocortical Daisy Architectures and Graphical Models for Context-Dependent Processing” FP6-2005-015803, by the German Federal Ministry of Education and Research (BMBF) within the “Bernstein Focus: Neurotechnology through research grant 01GQ0840” and by the Hertie Foundation. Conference: Bernstein Conference on Computational Neuroscience, Frankfurt am Main, Germany, 30 Sep - 2 Oct, 2009. Presentation Type: Poster Presentation Topic: Abstracts Citation: Sato Y, Jitsev J, Wolfrum P, Von Der Malsburg C and Morie T (2009). A Recurrent Network of Macrocolumnar Models for Face Recognition. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. doi: 10.3389/conf.neuro.10.2009.14.021 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 25 Aug 2009; Published Online: 25 Aug 2009. * Correspondence: Yasuomi Sato, Frankfurt Institute for Advanced Studies, Frankfurt, Germany, sato@fias.uni-frankfurt.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Yasuomi Sato Jenia Jitsev Philipp Wolfrum Christoph Von Der Malsburg Takashi Morie Google Yasuomi Sato Jenia Jitsev Philipp Wolfrum Christoph Von Der Malsburg Takashi Morie Google Scholar Yasuomi Sato Jenia Jitsev Philipp Wolfrum Christoph Von Der Malsburg Takashi Morie PubMed Yasuomi Sato Jenia Jitsev Philipp Wolfrum Christoph Von Der Malsburg Takashi Morie Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Similarity Effect and Optimal Control of Multiple-Choice Decision Making

Decision making with several choice options is central to cognition. To elucidate the neural mechanisms of such decisions, we investigated a recurrent cortical circuit model in which fluctuating spiking neural dynamics underlie trial-by-trial stochastic decisions. The model encodes a continuous analog stimulus feature and is thus applicable to multiple-choice decisions. Importantly, the continuous network captures similarity between alternatives and possible overlaps in their neural representation. Model simulations accounted for behavioral as well as single-unit neurophysiological data from a recent monkey experiment and revealed testable predictions about the patterns of error rate as a function of the similarity between the correct and actual choices. We also found that the similarity and number of options affect speed and accuracy of responses. A mechanism is proposed for flexible control of speed-accuracy tradeoff, based on a simple top-down signal to the decision circuit that may vary nonmonotonically with the number of choice alternatives.

Solving the Problem of Negative Synaptic Weights in Cortical Models

In cortical neural networks, connections from a given neuron are either inhibitory or excitatory but not both. This constraint is often ignored by theoreticians who build models of these systems. There is currently no general solution to the problem of converting such unrealistic network models into biologically plausible models that respect this constraint. We demonstrate a constructive transformation of models that solves this problem for both feedforward and dynamic recurrent networks. The resulting models give a close approximation to the original network functions and temporal dynamics of the system, and they are biologically plausible. More precisely, we identify a general form for the solution to this problem. As a result, we also describe how the precise solution for a given cortical network can be determined empirically.

Temporal Integration by Stochastic Recurrent Network Dynamics With Bimodal Neurons

Temporal integration of externally or internally driven information is required for a variety of cognitive processes. This computation is generally linked with graded rate changes in cortical neurons, which typically appear during a delay period of cognitive task in the prefrontal and other cortical areas. Here, we present a neural network model to produce graded (climbing or descending) neuronal activity. Model neurons are interconnected randomly by AMPA-receptor-mediated fast excitatory synapses and are subject to noisy background excitatory and inhibitory synaptic inputs. In each neuron, a prolonged afterdepolarizing potential follows every spike generation. Then, driven by an external input, the individual neurons display bimodal rate changes between a baseline state and an elevated firing state, with the latter being sustained by regenerated afterdepolarizing potentials. When the variance of background input and the uniform weight of recurrent synapses are adequately tuned, we show that stochastic noise and reverberating synaptic input organize these bimodal changes into a sequence that exhibits graded population activity with a nearly constant slope. To test the validity of the proposed mechanism, we analyzed the graded activity of anterior cingulate cortex neurons in monkeys performing delayed conditional Go/No-go discrimination tasks. The delay-period activities of cingulate neurons exhibited bimodal activity patterns and trial-to-trial variability that are similar to those predicted by the proposed model.

Criticality of avalanche dynamics in adaptive recurrent networks

In many studies of self-organized criticality (SOC), branching processes were used to model the dynamics of the activity of the system during avalanches. This mathematical simplification was also adopted when investigating systems with a complicated connection topology including recurrent and subthreshold interactions. However, none of these studies really analyzed whether this convenient approximation was indeed applicable. In present paper we study the correspondences between avalanches generated by branching processes and by a fully connected neural network. The benefit from the analysis is not only the justification of such correspondence but also a simple learning rule, which allows self-organization of the network towards a critical state as recently observed in slice experiments.

Dynamic recurrent wavelet network controllers for nonlinear system control

To solve nonlinear system control problems, a Recurrent Wavelet Network Controller (RWNC) is proposed in this paper. The proposed RWNC model has four‐layer structure. Temporal relations embedded in the network by adding some feedback connections representing the memory units in the second layer. A self‐organizing learning algorithm, which consists of structure learning and parameter learning, is proposed and is able to construct the recurrent wavelet network dynamically. The structure learning is based on the input partitions to determine the number of wavelet bases, and the parameter learning is based on the supervised gradient descent method to adjust the shape of wavelet functions, feedback weights, and the connection weights. Computer simulations were conducted to illustrate the performance and applicability of the proposed model.