Search

In this paper, some global exponential stability criteria for the equilibrium point of discrete-time recurrent neural networks with variable delay are presented by using the linear matrix inequality (LMI) approach. The neural networks considered are assumed to have asymmetric weighting matrices throughout this paper. On the other hand, by applying matrix decomposition, the model is embedded into a cooperative one, the latter possesses important order-preserving properties which are basic to our analysis. A sufficient condition is obtained ensuring the componentwise exponential stability of the system with specific performances such as decay rate and trajectory bounds. [ABSTRACT FROM AUTHOR]

Memristors are gaining increasing interest in the scientific community for their possible applications, e.g. high-speed low-power processors or new biological models for associative memories. Due to the intrinsic nonlinear characteristic of memristive devices, it is possible to use them in the design of new dynamical circuits that are able to show complex behavior, like chaos. In this paper, two new memristive chaotic circuits are presented discussing, in particular, an approach based on Cellular Nonlinear Networks for the implementation of the memristive device. The approach investigated in this paper allows to obtain memristors with common off-the-shelf components and to observe the onset of new chaotic attractors in nonlinear circuits with memristors. Furthermore, the circuits presented in this paper, being the first examples of memristive chaotic circuits based on CNNs, can be considered as the link between the three inventions by Leon O. Chua, i.e. the memristor, the first chaotic electronic circuit and Cellular Nonlinear Networks. [ABSTRACT FROM AUTHOR]

In 1998, Chen et al. [1998] found an error in Marotto's paper [1978]. It was pointed out by them that the existence of an expanding fixed point z of a map F in Br(z), the ball of radius r with center at z does not necessarily imply that F is expanding in Br(z). Subsequent efforts (see e.g. [Chen et al., 1998; Lin et al., 2002; Li & Chen, 2003]) in fixing the problems have some discrepancies since they only give conditions for which F is expanding "locally". In this paper, we give sufficient conditions so that F is "globally" expanding. This, in turn, gives more satisfying definitions of a snap-back repeller. We then use those results to show the existence of chaotic backward traveling waves in a discrete time analogy of one-dimensional Cellular Neural Networks (CNNs). Some computer evidence of chaotic traveling waves is also given. [ABSTRACT FROM AUTHOR]

This paper focuses on implementations of two modified Aihara's chaotic neuron models and a simple chaotic neural network constructed with two chaotic neurons in a programmable and reconfigurable manner with an analog programmable device, FPAA (Field Programmable Analog Array). After testing the chaotic behaviors of two chaotic neuron models and a simple chaotic neural network through numerical analyses that consist of time domain responses, phase portrait illustrations and bifurcation diagrams, the experimental setup is constructed with a FPAA device. The parametric adjustments of chaotic neural structures are possible with the proposed flexible design methodology and different chaotic neuron models are constructed on the same reconfigurable device without any hardware changes. Experimental results verify the dynamic behaviors of these chaotic neural structures and demonstrate the efficiency of programmable implementations. [ABSTRACT FROM AUTHOR]

This paper deals with a new type of synchronization scheme for chaotic neural networks with delays, called modified function projective synchronization, in which chaotic neural networks synchronize up to a scaling function matrix. Based on the nonlinear state observer, a control scheme is derived through the placement technique by designing a state-observer of the derived system to synchronize chaotic neural networks up to a scaling function matrix. This technique, capable of adjusting the scaling function factor arbitrarily for the value of scaling function factor, has no effect on the controllability of error system. That overcomes some limitation in earlier literature. A chaotic cellular neural network and a chaotic Hopfield neural model are used as numerical examples to demonstrate the effectiveness of the proposed synchronization technique. [ABSTRACT FROM AUTHOR]

In this paper, a hyperchaotic RTD-based cellular neural network is proposed and its hyperchaotic dynamics is demonstrated. The Lyapunov exponents spectrum is presented, and some typical Lyapunov exponents are calculated in a range of parameters. Several important phase portraits are presented as well. [ABSTRACT FROM AUTHOR]

This paper analyzes the generalized synchronization of chaotic neural networks and proposes an approach based on the Lyapunov stability theory. This approach realizes the generalized synchronization between two different dimensional neural networks. Numerical simulation examples are given to demonstrate the effectiveness of this approach. By the chaos-masking method, the simulation experiment about generalized synchronization of different dimensional neural networks in secure communication has verified the validity of the approach. [ABSTRACT FROM AUTHOR]

In this paper, we study a new class of simple three-neuron chaotic cellular neural networks with very simple connection matrices. To study the chaotic behavior in these cellular neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of the existence of horseshoe chaos using topological horseshoe theory and the estimate of topological entropy in derived Poincaré maps. [ABSTRACT FROM AUTHOR]

This paper presents a very versatile multifunction signal generator tool. The proposed generator is based on State Controlled Cellular Neural Network (SC-CNN) based Chua's circuit and it has two signal generation modes, namely CM (Chaos Mode) and FM (Function Mode). While the generator is able to produce nonlinear chaotic waveforms in Chaos Mode, it is also able to generate other classical sinusoidal, triangle and square waveforms in Function Mode. The proposed design idea has been validated through computer simulations and laboratory experiments. Future studies with the proposed generator tool will contribute to further developments in SC-CNN based engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we investigate global synchronization in an array of linearly coupled identical delayed neural networks. We consider the array with an arbitrary coupling matrix without assuming it to be symmetric, irreducible and diffusive. Moreover, we consider the array being connected through two different coupling schemes, state-coupling and output-coupling, respectively. For state-coupling, we derive a more general sufficient condition ensuring global synchronization, which is an extension of some existing results in the literature. For output-coupling, we derive a new sufficient condition for global synchronization. Numerical simulations are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a new class of chaotic and hyperchaotic low dimensional cellular neural networks modeled by ordinary differential equations with some simple connection matrices. The chaoticity of these neural networks is indicated by positive Lyapunov exponents calculated by a computer. [ABSTRACT FROM AUTHOR]

This paper addresses qualitative properties of equilibrium points in a class of delayed neural networks. We derive a sufficient condition for the local exponential stability of equilibrium points, and give an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons' activation functions and the associated equilibrium point; hence, they are easily checkable. Another advantage of our results is that they neither depend on monotonicity of the activation functions nor on symmetry of the interconnection matrix. Our work has practical importance in evaluating the performance of the related associative memory. To our knowledge, this is the first time to present an estimate on the domains of attraction of equilibrium points for delayed neural networks. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominally symmetric interconnections. More specifically, a class of circular one-dimensional (1-D) CNNs with nearest-neighbor interconnections only, is considered. The class has sparse interconnections and is subject to perturbations which preserve the interconnecting structure. Conditions assuring that the perturbed CNN has a unique equilibrium point at the origin, which is unstable, are provided in terms of relative magnitude of the perturbations with respect to the nominal interconnection weights. These conditions allow one to characterize regions in the perturbation parameter space where there is loss of stability for the perturbed CNN. In turn, this shows that even for sparse interconnections and structure preserving perturbations, robustness of complete stability is not guaranteed in the general case. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate hyperchaotic dynamics in a very simple Cellular Neural Network (CNN) which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, and the bifurcation plot is presented as well. [ABSTRACT FROM AUTHOR]

In this paper n-double scroll generating via diode-based PieceWise-Linear (PWL) circuit in State Controlled Cellular Neural Network (SC-CNN) is presented. It has been shown that by using simple diode-based configurations; alternative nonlinear circuit configurations for chaotic circuits and PWL-based systems can be used in the generation of n-double scrolls. With this study, while the analysis of the nonlinear block in the SC-CNN-based circuit is simplified, the implementation cost of the circuit is also reduced. Pspice simulations are proved with experimental studies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general class of discrete multiple-time delayed recurrent neural networks with external inputs. By applying a new transformation, we transform an m-neuron network model into a parameterized map from to . A chaotic invariant set of the neural networks system is obtained by using a family of projections from onto . Furthermore, we prove that the dynamics of this neural networks system restricted to the chaotic invariant set is topologically conjugate to the dynamics of the full shift map with two symbols, which indicates that chaos occurs. Numerical simulations are presented to illustrate the theoretical outcomes. [ABSTRACT FROM AUTHOR]

We analyze instantaneous stability of a chaotic neural network which shows nonperiodic associative dynamics. The network is composed of discrete-time neuron models of which individuals show chaotic dynamics with certain parameter values. The synaptic weights of the network are determined by an auto-associative matrix so that four binary patterns are stored as a basal memory of the network. It has been reported that the network retrieves stored patterns nonperiodically. However, the dynamical property of the network in each discrete-time step has not been clarified. In this paper, instantaneous stability of the network during the nonperiodic memory retrieval is analyzed by calculating eigenvalues of the Jacobian matrix. From the analysis, it is found that in every instance when the network retrieves stored patterns, all the eigenvalues are always less than unity. This implies that such states of the memory retrieval cannot be a target of the OGY-like chaos control methods. [ABSTRACT FROM AUTHOR]

In this paper a method for synchronizing high dimensional chaotic systems is developed. The objective is to generate a linear error dynamics between the master and the slave systems, so that synchronization is achievable by exploiting the controllability property of linear systems. The suggested approach is applied to Cellular Neural Networks (CNNs), which can be considered as a tool for generating complex hyperchaotic behaviors. Numerical simulations are carried out for synchronizing CNNs constituted by Chua's circuits. [ABSTRACT FROM AUTHOR]

In this paper, an arbitrary-dimensional quantum cellular neural network (QCNN) model and its fractional-order form are presented by using the polarization of quantum-dot cell and fractional derivatives. Two classes of fractional-order QCNN equations, either two-cell or three-cell models with different value of fractional order α are taken into consideration in detail. In particular, more complex and abundant fractional-order hyperchaotic behaviors can be observed by these two examples. Thus, the proposed fractional-order arbitrary-dimensional QCNN model can have an effective noninteger dimension and can generate rich hyperchaotic dynamics by nth cell. Numerical analysis and simulation results are provided to show the effectiveness of the proposed approach. This study provides valuable information about nth cell fractional-order QCNNs for further application in high-parallel signal processing and fractional quantum chaotic generators. [ABSTRACT FROM AUTHOR]

The peculiar features of the memristor, a fundamental passive two-terminal element characterized by a nonlinear relationship between charge and flux, promise to revolutionize integrated circuit design in the next few decades. Besides its most popular potential application, ultra-dense nonvolatile memories, much research has been lately devoted to their use in chaotic neural networks for the emulation of brain activity. In the studies on neuromorphic circuits, it is common to characterize each memristor with a theoretical model based upon a single-valued odd-symmetric charge-flux nonlinearity. Memristive nano-films exhibit different dynamics depending on the way they behave at boundaries. We recently developed a mathematical model, applicable to memristive nano-structures of various nature, offering the opportunity to tune the boundary conditions so as to capture a wide gamut of distinct nonlinear behaviors. However, in general the proposed model exhibits a multivalued charge-flux nonlinearity dependent on input and initial state condition. In this paper, we first derive the necessary and sufficient set of boundary conditions under which single-valuedness is observed in this nonlinearity for any input/state initial condition combination. Then, after proving that, under such boundary conditions, the asymmetrical nonlinearities of memristors with opposite orientation are the odd-symmetric function of the other, we devise a pair of suitable memristor arrangements with odd-symmetric charge-flux characteristics. This analysis is confirmed by showing how a chaotic neural circuit employing one of such arrangements behaves similarly to its counterpart with the theoretically-modeled memristor. [ABSTRACT FROM AUTHOR]

This paper studies the hyperchaotic dynamics in a four-dimensional Hopfield neural network by virtue of topological horseshoe. Two different horseshoes (chaotic invariant sets) are found in this network with the same parameters. Numerical studies show that the first one expands only one-dimensionally and the second one expands two-dimensionally. Computer simulation also shows that there exists a heteroclinic connection from the second horseshoe to the first one, which indicates that the chaotic set of this system can have a very complicated structure composed of different kinds of expansions. [ABSTRACT FROM AUTHOR]

An impulsive T–S fuzzy model is presented in this paper. The stability of impulsive controlled T–S fuzzy system has been analyzed theoretically. The proposed impulsive control scheme seems to have a simple control structure and may need less control energy than the normal continuous ones for the stabilization of T–S fuzzy system. Some typical chaotic systems, such as Chua's circuit, Lorenz system and Chen's chaotic system, are considered as illustrations to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a simulation of a biological olfactory neural system with a KIII set, which is a high-dimensional chaotic neural network. The KIII set differs from conventional artificial neural networks by use of chaotic attractors for memory locations that are accessed by, chaotic trajectories. It was designed to simulate the patterns of action potentials and EEG waveforms observed in electrophysiological experiments, and has proved its utility as a model for biological intelligence in pattern classification. An application to recognition of handwritten numerals is presented here, in which the classification performance of the KIII network under different noise levels was investigated. [ABSTRACT FROM AUTHOR]

This paper deals with computation over dynamical analog systems, exploring applications of chaos. The dynamical system used is an artificial neural network model that can code any symbolic algorithm. Herein, we propose the integration of chaotic dynamics onto this model, to implement computational tasks, namely, a blind search algorithm and a pseudo-random number generator. [ABSTRACT FROM AUTHOR]

This paper presents a neural network-based digital redesign approach for digital control of continuous-time chaotic systems with unknown structures and parameters. Important features of the method are that: (i) it generalizes the existing optimal linearization approach for the class of state-space models which are nonlinear in the state but linear in the input, to models which are nonlinear in both the state and the input; (ii) it develops a neural network-based universal optimal linear state-space model for unknown chaotic systems; (iii) it develops an anti-digital redesign approach for indirectly estimating an analog control law from a fast-rate digital control law without utilizing the analog models. The estimated analog control law is then converted to a slow-rate digital control law via the prediction-based digital redesign method; (iv) it develops a linear time-varying piecewise-constant low-gain tracker which can be implemented using microprocessors. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, an experimental implementation of State Controlled Cellular Neural Network (SC-CNN) circuit using Current Feedback Op Amp (CFOA) is presented and its chaotic dynamics including high frequency performance are investigated by laboratory experiments. Depending on its significant advantages over the conventional voltage op amps (VOAs), without imposing any restrictions, the CFOAs have been used instead of the VOAs in SC-CNN circuit. Experimental results have shown that the proposed implementation has a capacity of higher frequency operation. [ABSTRACT FROM AUTHOR]

A transiently chaotic neural network (TCNN) is an approximation method for combinatorial optimization problems. The evolution function of self-back connect weight, called annealing function, influences the accurate and search speed of TCNN model. This paper analyzes two common annealing schemes. Furthermore we proposed a new subsection exponential annealing function. Finally, we compared these annealing schemes in TSP problem. [ABSTRACT FROM AUTHOR]

This paper formulates the model and then studies its dynamics of a system of linearly and diffusively coupled identical delayed neural networks (DNNs), which is generalization of delayed Hopfied neural networks (DHNNs) and delayed cellular neural networks (DCNNs). In particularly, a simple yet generic sufficient condition for global synchronization of such coupled DNNs is derived based on the Lyapunov functional methods and Hermitian matrix theory. It is shown that global synchronization of coupled DNNs is ensured by a suitable design of the coupling matrix and the inner linking matrix. Furthermore, the result is applied to some typical chaotic neural networks. Finally, numerical simulations are presented to demonstrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of reconstructing a slowly-varying information-bearing signal from a parametrically modulated, nonstationary dynamical signal. A chaotic electronic oscillator model characterized by one control parameter and a double-scroll-like attractor is used throughout the study. Wavelet transforms are used to extract features of the chaotic signal resulting from parametric modulation of the control parameter by the useful signal. The vector of feature coefficients is fed into a feed-forward neural network that recovers the embedded information-bearing signal. The performance of the developed method is cross-validated through reconstruction of randomly-generated control parameter patterns. This method is applied to the reconstruction of speech signals, thus demonstrating its potential utility for secure communication applications. Our results are validated via numerical simulations. [ABSTRACT FROM AUTHOR]

The chaotic neural network constructed with chaotic neurons exhibits very rich dynamic behaviors and has a nonperiodic associative memory. In the chaotic neural network, however, it is difficult to distinguish the stored patters from others, because the states of output of the network are in chaos. In order to apply the nonperiodic associative memory into information search and pattern identification, etc, it is necessary to control chaos in this chaotic neural network. In this paper, the phase space constraint method focused on the chaotic neural network is proposed. By analyzing the orbital of the network in phase space, we chose a part of states to be disturbed. In this way, the evolutional spaces of the strange attractors are constrained. The computer simulation proves that the chaos in the chaotic neural network can be controlled with above method and the network can converge in one of its stored patterns or their reverses which has the smallest Hamming distance with the initial state of the network. The work clarifies the application prospect of the associative dynamics of the chaotic neural network. [ABSTRACT FROM AUTHOR]

In this paper, the Nagumo-Sato model is used to construct a chaotic neural network (CNN). Each reference sample is stored in the chaos attractor that is formed by the associative dynamics. When the inputs sometimes deviate obviously from its original attractive region and the correct association is not realized by itself, the feedback pinning is use to control the associative dynamics. The lost original memory will be retrieved quickly considering the fact that the CNN is a spatiotemporal system. The simulation experiments of both the associative dynamics and the retrieval process are done for the faults of broken rotor bars of an induction motor. The results show that the feedback pinning control is a simple and effective control method to the CNN. [ABSTRACT FROM AUTHOR]

Though chaotic behaviors are exhibited in many simple nonlinear models, physical chaotic systems are much more complex and contain many types of uncertainties. This paper presents a robust adaptive neural control scheme for a class of uncertain chaotic systems in the disturbed strict-feedback form, with both unknown nonlinearities and uncertain disturbances. To cope with the two types of uncertainties, we combine backstepping methodology with adaptive neural design and nonlinear damping techniques. A smooth singularity-free adaptive neural controller is presented, where nonlinear damping terms are used to counteract the disturbances. The differentiability problem in controlling the disturbed strict-feedback system is solved without employing norm operation, which is usually used in robust control design. The proposed controllers can be applied to a large class of uncertain chaotic systems in practical situations. Simulation studies are conducted to verify the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

By analogue of [Chen & Aihara, 1995, 1997, 1999], we theoretically investigate the topologically chaotic structure, attracting set and global searching ability of discrete-time recurrent neural networks with the form of u[sub i](t+1)=ku[sub i](t)+Δt(∑[sup n][sub j=1]a[sub ij]v[sub j](t)+a[sub i]) i = 1, 2, …, n where the input-output function is defined as a generalized sigmoid function, such as v[sub i] = tanh(µ[sub i]u[sub i]), v[sub i] = 2/π arctan (π/2 µ[sub i]u[sub i]) and v[sub i] = 1/1+e[sup -u[sub i]/ε] etc. We first derive sufficient conditions of existence for a fixed point, and then prove that this fixed point eventually evolves into a snap-back repeller which generates chaotic structure when certain conditions are satisfied. Furthermore we prove that there exists an attracting set which includes not only the homoclinic orbit but also the globally unstable set of fixed points, thereby ensuring the neural networks to have global searching ability. Numerical simulations are also provided to demonstrate the theoretical results. The results indicated in this paper can be viewed as an extension of the works of [Chen & Aihara, 1997, 1999] and others [Gopalsamy & He, 1994; Wang & Smith, 1998]. [ABSTRACT FROM AUTHOR]

In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated. [ABSTRACT FROM AUTHOR]

Chaotic burst synchronization in a two-small-world-layer neuronal network is studied in this paper. For a neuronal network coupled by two single-small-world-layer networks with link probability differences between layers, the two-layer network can achieve synchrony as the interlayer coupling strength increases. When chaotic layer network is coupled with chaotic-burst-synchronization layer network, the latter is dominant at small interlayer coupling strength, so it can make the layer with the irregular pattern show some regular and also exhibit the same pattern with the other layer. However, when chaotic layer is coupled with firing synchronization layer, the ordered layer is dominated by a disordered one with the interlayer coupling strength increasing. When the interlayer coupling strength is large enough, both networks are chaotic burst synchronization. Therefore, the synchronous states strongly depend on the interlayer coupling strength and the link probability. Moreover, the spatiotemporal pattern synchronization between the networks is robust to small noise. [ABSTRACT FROM AUTHOR]

The stochastic quasi-synchronization issue for uncertain chaotic delayed neural networks (DNNs) is investigated. Stochastic perturbation and three uncertain elements, including the discontinuous activation functions, mismatched connection weight parameters and unknown connection weight parameters, are considered in the chaotic DNNs. According to the Ito formula and the inequality techniques, the parameters update laws and the control laws are given to realize the synchronization. And a stochastic quasi-synchronization criterion is established. Furthermore, sufficient conditions are proposed for the control of the synchronization error bound by choosing appropriate control laws. Some numerical simulations are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Lag synchronization of bursting neuron systems is explored when the system is subjected to stochastic perturbation. An adaptive feedback control scheme is presented when the parameters of the neuron systems are unknown. At the same time, an adaptive control law is obtained via theoretical derivation so that two slightly mismatched chaotic systems achieved asymptotically lag synchronization. The effectiveness of the proposed scheme is not only confirmed by theoretical analysis, but also verified by numerical simulations. [ABSTRACT FROM AUTHOR]

The dynamic behavior of first-order autonomous space invariant cellular neural networks (CNNs) is investigated. It is shown that complex dynamics may occur in very simple CNN structures, described by two-dimensional templates that present only vertical and horizontal couplings. The bifurcation processes are analyzed through the computation of the limit cycle Floquet's multipliers, the evaluation of the Lyapunov exponents and of the signal spectra. As a main result a detailed and accurate two-dimensional bifurcation diagram is reported. The diagram allows one to distinguish several regions in the parameter space of a single CNN. They correspond to stable, periodic, quasi-periodic, and chaotic behavior, respectively. In particular it is shown that chaotic regions can be reached through two different routes: period doubling and torus breakdown. We remark that most practical CNN implementations exploit first order cells and space-invariant templates: so far only a few examples of complex dynamics and no complete bifurcation analysis have been presented for such networks. [ABSTRACT FROM AUTHOR]

Many real-world systems such as irregular ECG signal, volatility of currency exchange rate and heated fluid reaction exhibit highly complex nonlinear characteristic known as chaos. These chaotic systems cannot be retreated satisfactorily using linear system theory due to its high dimensionality and irregularity. This research focuses on prediction and modelling of chaotic FIR (Far InfraRed) laser system for which the underlying equations are not given. This paper proposed a method for prediction and modelling a chaotic FIR laser time series using rational function neural network. Three network architectures, TDNN (Time Delayed Neural Network), RBF (radial basis function) network and the RF (rational function) network, are also presented. Comparisons between these networks performance show the improvements introduced by the RF network in terms of a decrement in network complexity and better ability of predictability. [ABSTRACT FROM AUTHOR]

Bifurcations and chaos in a network of three identical sigmoidal neurons are examined. The network consists of a two-neuron oscillator of the Wilson–Cowan type and an additional third neuron, which has a simpler structure than chaotic neural networks in the previous studies. A codimension-two fold-pitchfork bifurcation connecting two periodic solutions exists, which is accompanied by the Neimark–Sacker bifurcation. A stable quasiperiodic solution is generated and Arnold's tongues emanate from the locus of the Neimark–Sacker bifurcation in a two-dimensional parameter space. The merging, splitting and crossing of the Arnold tongues are observed. Further, multiple chaotic attractors are generated through cascades of period-doubling bifurcations of periodic solutions in the Arnold tongues. The chaotic attractors grow and are destroyed through crises. Transient chaos and crisis-induced intermittency due to the crises are also observed. These quasiperiodic solutions and chaotic attractors are robust to small asymmetry in the output function of neurons. [ABSTRACT FROM AUTHOR]

Artificial neural networks (ANNs) are implemented in hardware when software implementations are inadequate in terms of performance. Implementing an ANN as hardware without using design automation tools is a time consuming process. On the other hand, this process can be automated using pre-designed neurons. Thus, in this work, several artificial neural cells were designed and implemented to form a library of neurons for rapid realization of ANNs on FPGA-based embedded systems. The library contains a total of 60 different neurons, two-, four- and six-input biased and non-biased, with each having 10 different activation functions. The neurons are highly pipelined and were designed to be connected to each other like Lego pieces. Chip statistics of the neurons showed that depending on the type of the neuron, about 25 selected neurons can be fit in to the smallest Virtex-6 chip and an ANN formed using the neurons can be clocked up to 576.89MHz. ANN based Rössler system was constructed to show the effectiveness of using neurons in rapid realization of ANNs on embedded systems. Our experiments with the neurons showed that using these neurons, ANNs can rapidly be implemented as hardware and design time can significantly be reduced. [ABSTRACT FROM AUTHOR]

The chaotic spiking and intermittent chaotic bursting were observed from biological experiment on a neural pacemaker. The intermittent chaotic bursting manifested alternation between a phase of nearly period-3 bursting and another phase of irregular bursting, and exhibited a nonsmooth-like structure in the first return map of interspike interval (ISI) series. The chaotic spiking manifested a smooth structure. The intermittent chaotic bursting and spiking simulated in the Chay model were identified by the dissection of the fast-slow variables. The intermittent chaotic bursting manifested nonsmooth-like structures in the first return map of both ISI and slow variable, while spiking exhibited smooth structures. The intermittent chaotic bursting and spiking manifested different scale laws of the averaged length of periodic phase with respect to the changes of parameter value. The scale law of bursting was similar to those of both type V intermittent chaos generated in a nonsmooth map and type I in a smooth system, while that of spiking resembled type I more than type V. The results revealed the dynamics of intermittent chaotic firing patterns, the differences between the intermittent chaotic bursting and spiking patterns and the relationships to the smooth and nonsmooth-like characteristics, provided a deep understanding of intermittent chaotic firing patterns, and indicated different mechanisms of the adjustment of variables from slow to fast between bursting and spiking patterns. [ABSTRACT FROM AUTHOR]

Chaos entanglement is a new approach to connect linear systems to chaos. The basic principle is to entangle two or multiple linear systems by nonlinear coupling functions to form an artificial chaotic system/network such that each of them evolves in a chaotic manner. However, it is only applicable for stable linear systems, not for unstable ones because of the divergence property. In this study, a bound function is introduced to bound the unstable linear systems and then chaos entanglement is realized in this scenario. Firstly, a new 6-scroll attraetor, entangling three identi-cal unstable linear systems by sine function, is presented as an example. The dynamical analysis shows that all entangled subsystems are bounded and their equilibrium points are unstable sad-dle points when chaos entanglement is achieved. Also, numerical computation exhibits that this new attraetor possesses one positive Lyapunov exponent, which implies chaos. Furthermore, a 4 x 4 x 4-grid attraetor is generalized by introducing a more complex bound function. Hybrid entanglement is obtained when entangling a two-dimensional stable linear subsystem and a one-dimensional unstable linear subsystem. Specifically, it is verified that it is possible to produce chaos by entangling unstable linear subsystems through linear coupling functions -- a special approach referred to as linear entanglement. A pair of 2-scroll chaotic attractors are established by linear entanglement. Our results indicate that chaos entanglement is a powerful approach to generate chaotic dynamics and could be utilized as a guideline to effectively create desired chaotic systems for engineering applications. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel method for reducing the attributes of sensory datasets using Master-Slave Synchronization of chaotic Lorenz Systems (DPSMS). As part of the performance testing, three benchmark datasets and one Electronic Nose (EN) sensory dataset with 3 to 13 attributes were presented to our algorithm to be projected into two attributes. The DPSMS-processed datasets were then used as input vector to four artificial intelligence classifiers, namely Feed-Forward Artificial Neural Networks (FFANN), Multilayer Perceptron (MLP), Decision Tree (DT) and K-Nearest Neighbor (KNN). The performance of the classifiers was then evaluated using the original and reduced datasets. Classification rate of 94.5%, 89%, 94.5% and 82% were achieved when reduced Fishers iris, crab gender, breast cancer and electronic nose test datasets were presented to the above classifiers. [ABSTRACT FROM AUTHOR]

Chaos, bifurcation and robustness of a new class of Hopfield neural networks are investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, the bifurcation plot and several important phase portraits are presented as well. By virtue of horseshoes theory in dynamical systems, rigorous computer-assisted verifications for chaotic behavior of the system with certain parameters are given, and here also presents a discussion on the robustness of the original system. Besides this, quantitative descriptions of the complexity of these systems are also given, and a robustness analysis of the system is presented too. [ABSTRACT FROM AUTHOR]