Complex dynamics in a Hopfield neural network under electromagnetic induction and electromagnetic radiation

Heterogeneous coexisting attractors, large-scale amplitude control and finite-time synchronization of central cyclic memristive neural networks

Memristors are of great theoretical and practical significance for chaotic dynamics research of brain-like neural networks due to their excellent physical properties such as brain synapse-like memorability and nonlinearity, especially crucial for the promotion of AI big models, cloud computing, and intelligent systems in the artificial intelligence field. In this paper, we introduce memristors as self-connecting synapses into a four-dimensional Hopfield neural network, constructing a central cyclic memristive neural network (CCMNN), and achieving its effective control. The model adopts a central loop topology and exhibits a variety of complex dynamic behaviors such as chaos, bifurcation, and homogeneous and heterogeneous coexisting attractors. The complex dynamic behaviors of the CCMNN are investigated in depth numerically by equilibrium point stability analysis as well as phase trajectory maps, bifurcation maps, time-domain maps, and LEs. It is found that with the variation of the internal parameters of the memristor, asymmetric heterogeneous attractor coexistence phenomena appear under different initial conditions, including the multi-stable coexistence behaviors of periodic-periodic, periodic-stable point, periodic-chaotic, and stable point-chaotic. In addition, by adjusting the structural parameters, a wide range of amplitude control can be realized without changing the chaotic state of the system. Finally, based on the CCMNN model, an adaptive synchronization controller is designed to achieve finite-time synchronization control, and its application prospect in simple secure communication is discussed. A microcontroller-based hardware circuit and NIST test are conducted to verify the correctness of the numerical results and theoretical analysis.

Dynamics of heterogeneous Hopfield neural network with adaptive activation function based on memristor

Memristor and activation function are two important nonlinear factors of the memristive Hopfield neural network. The effects of different memristors on the dynamics of Hopfield neural networks have been studied by many researchers. However, less attention has been paid to the activation function. In this paper, we present a heterogeneous memristive Hopfield neural network with neurons using different activation functions. The activation functions include fixed activation functions and an adaptive activation function, where the adaptive activation function is based on a memristor. The theoretical and experimental study of the neural network's dynamics has been conducted using phase portraits, bifurcation diagrams, and Lyapunov exponents spectras. Numerical results show that complex dynamical behaviors such as multi-scroll chaos, transient chaos, state jumps and multi-type coexisting attractors can be observed in the heterogeneous memristive Hopfield neural network. In addition, the hardware implementation of memristive Hopfield neural network with adaptive activation function is designed and verified. The experimental results are in good agreement with those obtained using numerical simulations.

Simple cyclic memristive neural networks with coexisting attractors and large-scale amplitude control

The memristor's unique memory function and non-volatile nature make it an ideal electronic bionic device for artificial neural synapses. This paper aims to construct a class of memristive neural networks (MNNs) with a simple circular connection relationship and complex dynamics by introducing a generic memristor as synapse. For placing the memristive synapse in different coupling positions, three MNNs with the same coupling cyclic connection are yielded. One remarkable feature of the proposed MNNs is that they can yield complex dynamics, in particular, abundant coexisting attractors and large-scale parameter-relied amplitude control, by comparing with some existing MNNs. Taking one of the MNNs as an example, the complex dynamics (including chaos, period-doubling bifurcation, symmetric coexisting attractors, large-scale amplitude control) and circuit implementation are studied . The number of equilibria and their stabilities are discussed. The parameter-relied dynamic evolution and the coexisting attractors are numerically shown by using bifurcations and phase portraits. A microcontroller-based hardware circuit is given to realize the network, which verifies the correctness of the numerical results and experimental results.

An Inductorless Gain-Controllable Wideband LNA Based on CCCIIs

In this paper, an inductorless and gain-controllable 0.5~2.5 GHz wideband low noise amplifier (LNA) based on second generation current controlled current conveyors (CCCIIs) is presented. The proposed wideband LNA utilizes CCCIIs as building blocks to implement the amplifier stage and impedance matching stage. By varying the DC biasing current of the CCCII, the voltage gain of the proposed LNA is controllable in the range of 1~18 dB. In the frequency range of 0.5~2.5 GHz, the post-layout simulation results show that the proposed LNA has a typical voltage gain S21 of 12.6 dB with a gain ripple of ±1.5 dB, an input and output return loss (S11 and S22) of, respectively, -21.4 dB to -16.6 dB and -18.6 dB to -10.6 dB, and a high reverse isolation S12 of -65.2 dB to -39.5 dB. A noise figure of 4.05~4.35 dB is obtained across the whole band, and the input third-order intercept point (IIP3) is -2.5 dBm at 1.5 GHz. Using a 0.18 μm RF CMOS technology, the LNA occupies an active chip area of only 0.096 mm² with a power consumption of 12.0 mW.

A novel activation function based recurrent neural networks and their applications on sentiment classification and dynamic problems solving

In this paper, a nonlinear activation function (NAF) is proposed to constructed three recurrent neural network (RNN) models (Simple RNN (SRNN) model, Long Short-term Memory (LSTM) model and Gated Recurrent Unit (GRU) model) for sentiment classification. The Internet Movie Database (IMDB) sentiment classification experiment results demonstrate that the three RNN models using the NAF achieve better accuracy and lower loss values compared with other commonly used activation functions (AF), such as ReLU, SELU etc. Moreover, in terms of dynamic problems solving, a fixed-time convergent recurrent neural network (FTCRNN) model with the NAF is constructed. Additionally, the fixed-time convergence property of the FTCRNN model is strictly validated and the upper bound convergence time formula of the FTCRNN model is obtained. Furthermore, the numerical simulation results of dynamic Sylvester equation (DSE) solving using the FTCRNN model indicate that the neural state solutions of the FTCRNN model quickly converge to the theoretical solutions of DSE problems whether there are noises or not. Ultimately, the FTCRNN model is also utilized to realize trajectory tracking of robot manipulator and electric circuit currents computation for the further validation of its accurateness and robustness, and the corresponding results further validate its superior performance and widespread applicability.

Dynamics study on the effect of memristive autapse distribution on Hopfield neural network

As the shortest feedback loop of the nervous system, autapse plays an important role in the mode conversion of neurodynamics. In particular, memristive autapses can not only facilitate the adjustment of the dynamical behavior but also enhance the complexity of the nervous system, in view of the fact that the dynamics of the Hopfield neural network has not been investigated and studied in detail from the perspective of memristive autapse. Based on the traditional Hopfield neural network, this paper uses a locally active memristor to replace the ordinary resistive autapse so as to construct a 2 n-dimensional memristive autaptic Hopfield neural network model. The boundedness of the model is proved by introducing the Lyapunov function and the stability of the equilibrium point is analyzed by deriving the Jacobian matrix. In addition, four scenarios are established on a small Hopfield neural network with three neurons, and the influence of the distribution of memristive autapses on the dynamics of this small Hopfield neural network is described by numerical simulation tools. Finally, the Hopfield neural network model in these four situations is designed and implemented on field-programmable gate array by using the fourth-order Runge-Kutta method, which effectively verifies the numerical simulation results.