Cellular Neural Network Cell Research Articles

Bionic firing activities in a dual mem-elements based CNN cell

Firing activities provide the potential possibility for achieving bio-brain functionality with high energy-efficient and high-speed information processing performance. This inspires the design of bionic circuits to generate firing activities and develop brain-like applications. In this paper, a dual mem-elements based cellular neural network (CNN) cell is constructed to produce bionic firing activities, in which a non-ideal memcapacitor and an N-type locally active memristor are employed to emulate the functions of the neuronal membrane. The proposed CNN cell has an excitation-dependent equilibrium trajectory and stability. Numerical analysis shows that the dual mem-elements based CNN cell has abundant dynamical behaviors of forward/reverse period-doubling bifurcation routes, chaos crisis, tangent bifurcation, and bubbles with the change of model parameters of the CNN cell, memcapacitor, and exciting source. As a result, the rich firing patterns’ transition can be observed from the two-dimensional dynamics evolution. The analog circuit of the proposed CNN cell is designed, and then a PCB-based hardware circuit is implemented. The experimental results certify the accuracy of the theoretical and numerical analysis.

Biphasic action potentials in an individual cellular neural network cell

Hardware circuit that can effectively simulate biological neurons is an important basis for neuromorphic computation. Cellular neural network (CNN) cell is the basic information processor of a CNN, which acts like a neuron in the brain and has good circuit realizability. An individual memristive CNN cell is constructed by using a memristor instead of a linear resistor for imitating the ion channel time-varying conductance, in which abundant biphasic chaotic and periodic spiking activities are uncovered. This provides a new way to simulate biological neurons at the level of analog circuits. This paper first deduces the mathematical model of the memristive CNN cell, analyzes the equilibrium stability and then explores its dynamical behaviors based on numerical simulation. The results display that the different spiking activities can be effectively regulated by the system parameters and excitation parameters. Furthermore, the analog circuit of the memristive CNN cell is designed and the PSpice-based circuit simulations are performed to verify the correctness of the numerical simulations.

Multi-stable states and synchronicity of a cellular neural network with memristive activation function

The cellular neural network (CNN) is an implementable solution for fully connected neural networks. Using nanoscale memristor to realize its nonlinear activation function can simplify the circuit implementation of CNN effectively. This paper presents a paradigm of the basic CNN cell by introducing a voltage-controlled memristor as the activating module of its output circuit. A three-cell memristor-based CNN (mCNN) is constructed to demonstrate the parameter- and initial condition-influenced dynamical behaviors induced by the activating memristor. Furtherly, two identical three-cell mCNNs are chosen as the subnets to construct a memristor-coupled mCNN, based on which the multi-stable states and the synchronous behaviors are investigated. Numerical results show that the multi-stable states of the memristor-coupled mCNN are flexibly switched by adjusting the coupling strength and initial conditions. Under the control of the memristor coupler, the two subnets can achieve complete synchronization, lag synchronization and phase synchronization. Finally, the FPGA-based hardware experiments are executed to verify the numerical results.

An Analytical and Experimental Study of SC-CNN-Based Simple Nonautonomous Chaotic Circuit

Abstract In this study, we report an explicit analytical solution of state-controlled cellular neural network (SC-CNN) based second-order nonautonomous system. The proposed system is modeled with an aid of a generalized two-state-controlled cellular neural network (CNN) equations and experimentally realized by imposing a suitable connection of simple two-state-controlled generalized CNN cells following the report of Swathi et al. [2014]. The chaotic and quasi-periodic dynamics observed from this system have been investigated through an analytical approach for the first time. The intriguing dynamics observed from the system where further substantiated by phase portraits, Poincaré map, power spectra, and “0−1 test.” We trace the transition of the system from periodic to chaos through analytical solutions, which are in good agreement with hardware experiments. Additionally, we show PSpice circuit simulation results for validating our analytical and experimental studies.

Complete stability of feedback CNNs with dynamic memristors and second‐order cells

SummaryThe paper considers a feedback cellular neural network (CNN) obtained by interconnecting elementary cells with an ideal capacitor and an ideal flux‐controlled memristor. It is supposed that during the analogue computation of the CNN the memristors behave as dynamic elements, so that each dynamic memristor (DM)‐CNN cell is described by a second‐order differential system in the state variables given by the capacitor voltage and the memristor flux. The proposed networks are called DM‐CNNs, that is CNNs using a dynamic (D) memristor (M). After giving a foundation to the DM‐CNN model, the paper establishes a fundamental result on complete stability, that is convergence of solutions toward equilibrium points, when the DM‐CNN has symmetric interconnections. Because of the presence of dynamic memristors, a DM‐CNN displays peculiar and basically different dynamic properties with respect to standard CNNs. First of all a DM‐CNN computes during the time evolution of the memristor fluxes, instead of the capacitor voltages as for a standard CNN. Furthermore, when a steady state is reached, the memristors keep in memory the result of the computation, that is the limiting values of the fluxes, while all memristor currents and voltages, as well as all currents, voltages, and power in the DM‐CNN vanish. Instead, for standard CNNs, currents, voltages, and power do not drop off when a steady state is reached. Copyright © 2016 John Wiley & Sons, Ltd.

On the Impact of Energy-Accuracy Tradeoff in a Digital Cellular Neural Network for Image Processing

This paper studies the opportunities of energy-accuracy tradeoff in cellular neural network (CNN). Algorithmic characteristics of CNN is coupled with hardware-induced error distribution of a digital CNN cell to evaluate energy-accuracy tradeoff for simple image processing tasks as well as a complex application. The analysis shows that errors modulate the cell dynamics and propagate through the network degrading the output quality and increasing the convergence time. The error propagation is determined by the task being performed by the CNN, specifically, the strength of the feedback template. Controlling precision is observed to be a more effective approach for energy-accuracy tradeoff in CNN than voltage over scaling.

Multilayer RTD-memristor-based cellular neural networks for color image processing

Multilayer cellular neural networks (CNNs) with multiple state variables in each cell associated with multiple dynamic rules are believed to possess more powerful data computing and signal processing capabilities than single-layer CNNs and are specially suitable for solving complex problems. However, at present, their large scale integrated hardware implementation is still quite challenging based on traditional CMOS-based technology due to high circuity complexity and their applications are thus limited in practice. In this paper, a novel compact multilayer CNN model based on nanometer scale resonant tunneling diodes (RTDs) and memristors is presented. More specifically, in this model, one multilayer CNN cell consists of several sub-cells located in different layers. The resonant tunneling diode with quantum tunneling induced nonlinearity and uniquely folded current–voltage characteristics is used to implement the compact and high-speed cell via replacing the original linear resistor and removing the output function of conventional CNN cells. Furthermore, the interactions between these cells are determined by a pair of multi-dimensional cloning templates. And a compact synaptic circuit based on memristors is designed to realize the cloning template parameter (weight strength) and the multiplication (weighting) operation, by leveraging its nonvolatility, good scalability, and variable conductance. The combination of these desirable elements equips the proposed multilayer CNN with advantages of powerful processing capability as well as high compactness, versatility, and possibility of very large scale integration (VLSI) circuit implementations. Finally, the performance of the proposed multilayer CNN is validated by five illustrative examples in color image processing with each layer dealing with each primary color (red, green or blue) plane.

A new design for reconfigurable XOR function based on cellular neural networks

We have described a new method to construct the reconfigurable XOR logic circuit by using the modification of the standard uncoupled cellular neural network (CNN) cells. The modification of the cell is easier to implement in engineering applications. The scheme proposed in this paper, using the modification of standard uncoupled CNN cells, allows less hardware consumption in comparison to the utilisation of chaos computing system or harnessing piecewise-linear systems. The template parameters of the modified cell have been discussed, and the physical circuit implementing the reconfigurable two-input and three-input XOR function has also been presented.

Stability of Equilibrium Points in Cellular Neural Networks with Negative Slope Activation Function

In the paper, the region of the number of equilibrium points of every cell in cellular neural networks with negative slope activation function is considered by the relationship between parameters of cellular neural networks. Some sufficient conditions are obtained by using the relationship among connection weights. Three theorems and a corollary are gotten by our new methods. Depending on these sufficient conditions, inputs and outputs of a CNN, the regions of the values of parameters can be obtained. Some numerical simulations are presented to support the effectiveness of the theoretical analysis.

Hybrid memristor/RTD structure-based cellular neural networks with applications in image processing

Cellular neural network (CNN) has been acted as a high-speed parallel analog signal processor gradually. However, recently, since the decrease in the size of transistor is going to approach the utmost, the transistor-based integrated circuit technology hits a bottleneck. As a result, the advantage of very large scale integration implementation of CNN becomes hard to really present, and further development of this era faces severe challenges unavoidably. In this study, two types of memristor-based cellular neural networks have been proposed. One type uses a memristor to replace the linear resistor in a conventional CNN cell circuit. And the other places a resonant tunneling diode (RTD) in this position and uses memristive synaptic connections to structure a hybrid memristor RTD CNN model. The excellent performances of the proposed CNNs are verified by conventional means of, for instance, stability analysis and efficient applications in image processing. Since both the memristor and the resonant tunneling diode are nanoscale, the size of the network circuits can be greatly reduced, and the integration density of the system will be significantly improved.

Analysis on Cellular Neural Networks with Negative Slope Activation Function

In the paper, the region of the number of equilibrium points of every cell in cellular neural networks with negative slope activation function is considered by the relationship between parameters of cellular neural networks. Some conditions are obtained by using the relationship among connection weights. Depending on these sufficient conditions, inputs and outputs of a CNN, the regions of the values of parameters can be obtained. Some numerical simulations are presented to support the effectiveness of the theoretical analysis.

A Novel General and Robust Method Based on NAOP for Solving Nonlinear Ordinary Differential Equations and Partial Differential Equations by Cellular Neural Networks

This paper develops and validates through a series of presentable examples, a comprehensive high-precision, and ultrafast computing concept for solving nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs) with cellular neural networks (CNN). The core of this concept is a straightforward scheme that we call "nonlinear adaptive optimization (NAOP),” which is used for a precise template calculation for solving nonlinear ODEs and PDEs through CNN processors. One of the key contributions of this work is to demonstrate the possibility of transforming different types of nonlinearities displayed by various classical and well-known nonlinear equations (e.g., van der Pol-, Rayleigh-, Duffing-, Rössler-, Lorenz-, and Jerk-equations, just to name a few) unto first-order CNN elementary cells, and thereby enabling the easy derivation of corresponding CNN templates. Furthermore, in the case of PDE solving, the same concept also allows a mapping unto first-order CNN cells while considering one or even more nonlinear terms of the Taylor's series expansion generally used in the transformation of a PDE in a set of coupled nonlinear ODEs. Therefore, the concept of this paper does significantly contribute to the consolidation of CNN as a universal and ultrafast solver of nonlinear ODEs and/or PDEs. This clearly enables a CNN-based, real-time, ultraprecise, and low-cost computational engineering. As proof of concept, two examples of well-known ODEs are considered namely a second-order linear ODE and a second order nonlinear ODE of the van der Pol type. For each of these ODEs, the corresponding precise CNN templates are derived and are used to deduce the expected solutions. An implementation of the concept developed is possible even on embedded digital platforms (e.g., field programmable gate array (FPGA), digital signal processor (DSP), graphics processing unit (GPU), etc.). This opens a broad range of applications. Ongoing works (as outlook) are using NAOP for deriving precise templates for a selected set of practically interesting ODEs and PDEs equation models such as Lorenz-, Rössler-, Navier Stokes-, Schrödinger-, Maxwell-, etc.

Analysis on equilibrium points of cells in cellular neural networks described using cloning templates

In the paper, the region of the number of equilibrium points of a cell in cellular neural networks is considered by the relationship between parameters of cellular neural networks. The number of equilibrium points can be obtained by our results, and we also find that the values of connection weights of CNNs have an influence on the number of equilibrium points for a cell. A design procedure of parameters of cellular neural networks is given. Finally, some numerical simulations are presented to support the effectiveness of the theoretical analysis.

CNN‐based ultrafast solver of stiff ODEs and PDEs for enabling realtime Computational Engineering

PurposeThis paper seeks to develop, propose and validate, through a series of presentable examples, a comprehensive high‐precision and ultra‐fast computing concept for solving stiff ordinary differential equations (ODEs) and partial differential equations (PDEs) with cellular neural networks (CNN).Design/methodology/approachThe core of the concept developed in this paper is a straight‐forward scheme that we call “nonlinear adaptive optimization (NAOP)”, which is used for a precise template calculation for solving any (stiff) nonlinear ODEs through CNN processors.FindingsOne of the key contributions of this work (this is a real breakthrough) is to demonstrate the possibility of mapping/transforming different types of nonlinearities displayed by various classical and well‐known oscillators (e.g. van der Pol‐, Rayleigh‐, Duffing‐, Rössler‐, Lorenz‐, and Jerk‐ oscillators, just to name a few) unto first‐order CNN elementary cells, and thereby enabling the easy derivation of corresponding CNN‐templates. Furthermore, in case of PDEs solving, the same concept also allows a mapping unto first‐order CNN cells while considering one or even more nonlinear terms of the Taylor's series expansion generally used in the transformation of a PDEs in a set of coupled nonlinear ODEs. Therefore, the concept of this paper does significantly contribute to the consolidation of CNN as a universal and ultra‐fast solver of stiff differential equations (both ODEs and PDEs). This clearly enables a CNN‐based, real‐time, ultra‐precise, and low‐cost Computational Engineering. As proof of concept a well‐known prototype of stiff equations (van der Pol) has been considered; the corresponding precise CNN‐templates are derived to obtain precise solutions of this equation.Originality/valueThis paper contributes to the enrichment of the literature as the relevant state‐of‐the‐art does not provide a systematic and robust method to solve nonlinear ODEs and/or nonlinear PDEs using the CNN‐paradigm. Further, the “NAOP” concept developed in this paper has been proven to perform accurate and robust calculations. This concept is not based on trial‐and‐error processes as it is the case for various classes of optimization methods/tools (e.g. genetic algorithm, particle swarm, neural networks, etc.). The “NAOP” concept developed in this frame does significantly contribute to the consolidation of CNN as a universal and ultra‐fast solver of nonlinear differential equations (both ODEs and PDEs). An implantation of the concept developed is possible even on embedded digital platforms (e.g. field‐programmable gate array (FPGA), digital signal processing (DSP), graphics processing unit (GPU), etc.); this opens a broad range of applications. On‐going works (as outlook) are using NAOP for deriving precise templates for a selected set of practically interesting PDE models such as Navier Stokes, Schrödinger, Maxwell, etc.

Preliminary results from an analog implementation of first‐order TDCNN dynamics

AbstractThis work falls into the category of linear cellular neural network (CNN) implementations. We detail the first investigative attempt on the CMOS analog VLSI implementation of a recently proposed network formalism, which introduces time‐derivative ‘diffusion’ between CNN cells for nonseparable spatiotemporal filtering applications—the temporal‐derivative CNNs (TDCNNs). The reported circuit consists of an array of Gm‐C filters arranged in a regular pattern across space. We show that the state–space coupling between the Gm‐C‐based array elements realizes stable and linear first‐order (temporal) TDCNN dynamics. The implementation is based on linearized operational transconductance amplifiers and Class‐AB current mirrors. Measured results from the investigative prototype chip that confirms the stability and linearity of the realized TDCNN are provided. The prototype chip has been built in the AMS 0.35 µm CMOS technology and occupies a total area of 12.6 mm sq, while consuming 1.2 µW per processing cell. Copyright © 2010 John Wiley & Sons, Ltd.

A CNN-Specific Integrated Processor

Integrated Processors (IP) are algorithm-specific cores that either by programming or by configuration can be re-used within many microelectronic systems. This paper looks at Cellular Neural Networks (CNN) to become realized as IP. First current digital implementations are reviewed, and the memoryprocessor bandwidth issues are analyzed. Then a generic view is taken on the structure of the network, and a new intra-communication protocol based on rotating wheels is proposed. It is shown that this provides for guaranteed high-performance with a minimal network interface. The resulting node is small and supports multi-level CNNdesigns, giving the systema 30-fold increase in capacity compared to classical designs. As it facilitates multiple operations on a single image, and single operations on multiple images, with minimal access to the external image memory, balancing the internal and external data transfer requirements optimizes the system operation. In conventional digital CNN designs, the treatment of boundary nodes requires additional logic to handle the CNN value propagation scheme. In the new architecture, only a slight modification of the existing cells is necessary to model the boundary effect. A typical prototype for visual pattern recognition will house 4096 CNN cells with a 2% overhead for making it an IP.

High-performance Viterbi decoder with circularly connected 2-D CNN unilateral cell array

A very-high-performance Viterbi decoder with a circularly connected two-dimensional analog cellular neural network (CNN) cell array is disclosed. In the proposed Viterbi decoder, the CNN cells with nonlinear unilateral connections are implemented with electronic circuits at nodes on a trellis diagram. The circuits are circularly connected, forming a cylindrical shape so that the cells of the last stage are connected to those of the first stage. Unilateral connections guide the information to flow circularly around the cylindrical surface. Such configuration enables the conceptually infinite length of the trellis diagram to be reduced to a circuit of limited size. The analog circuits does not require any analog-digital converters, which is the major cause of high power consumption and the quantization error. With the parallel analog processing structure, its decoding speed becomes very high. Also, the decoding mechanism using triggering wave of the CNN circuit does not require the path memory. Circuits for the proposed structure have been designed with HSPICE. Features of the proposed Viterbi decoder are compared with those of the conventional digital Viterbi decoder.

Analog CMOS implementation of a CNN-based locomotion controller with floating-gate devices

This paper proposes an analog CMOS circuit that implements a central pattern generator (CPG) for locomotion control in a quadruped walking robot. Our circuit is based on an affine transformation of a reaction-diffusion cellular neural network (CNN), and uses differential pairs with multiple-input floating-gate (MIFG) MOS transistors to implement both the nonlinearity and summation of CNN cells. As a result, the circuit operates in voltage mode, and thus it is expected to reduce power consumption. Due to good matching accuracy of devices, the circuit generates stable rhythmic patterns for robot locomotion control. From experimental results on fabricated chip using a standard CMOS 1.5-/spl mu/m process, we show that the chip yields the desired results; i.e., stable rhythmic pattern generation and low power consumption.

MULTIPURPOSE HYSTERESIS CNN

In this paper, we propose a multipurpose hysteresis CNN (cellular neural network) made of first-order cells with hysteresis switches. The hysteresis CNN has applications not only in image processing, but also in pattern formation, nonlinear wave propagation and associative and dynamic memories, because each hysteresis CNN cell has two operating modes, namely, a bistable multivibrator mode and a relaxation oscillator mode.

A CMOS Implementation of a 1-Bit Multi-Cell Encoded—Cellular Neural Network

A new Cellular Neural Network (CNN)-based system has been implemented and tested to demonstrate the ability of this novel system to process large digital images more rapidly than its conventional CNN counterpart. The multi-cell encoded CNN processes the data of multiple single-data CNN cells within each multi-cell encoded cell enabling the new architecture it's advantages in loading, processing, unloading speed and in layout. A one bit (1B) 4-cell-encoded CNN was implemented to illustrate this new system. In this CMOS implementation, data of four neighboring conventional 1B CNN cells are encoded for processing within encoded cells. The CMOS circuits and circuit networks of one encoded cell are presented. Due to area limitations, each test chip includes the hardware for only one one-dimensional encoded cell. Experimental results of one-chip and two-chip 1B, multi-cell encoded systems are presented for connected-component detection and edge detection test cases. These results demonstrate the correct response of this implementation due to variations in template values, boundary values, and initial conditions. Interactions between encoded cell components and encoded cells are demonstrated for both dynamic and static responses. This CMOS implementation validates this new CNN architecture and provides a template for implementations using more advanced device technologies and circuits.