Dynamics analysis, hardware implementation and engineering applications of novel multi-style attractors in a neural network under electromagnetic radiation

Abstract This article studies the interesting dynamics of a small neural network with three neurons under electromagnetic radiation. The electromagnetic radiation strength can change the number of the equilibrium points in the neural network, which leads to the diversification of the attractor’s trajectory. Thus, the novel multi-style attractors like one-to-two-spiral attractors and one-to-four-scroll attractors can be generated from the neural network stimulated by electromagnetic radiation. Besides, the plentiful dynamical behaviors are observed in the neural network, such as transitional coexisting attractors, hypogenetic attractors, periodic patterns, firing patterns, transient chaos and intermittent chaos. In terms of hardware implementation, we utilize FPGA to digitally implement the constructed neural network model. The experimental verification results are highly consistent with the numerical simulation results. In the aspects of engineering application, we apply it to pseudo-random number generator and image encryption respectively, test the random performance of different chaotic attractors by NIST test suite, describe the image encryption scheme based on neural network and estimate its security performances. The ultimate outcomes demonstrate that the neural network model with chaotic behavior has superior randomness and wonderful security, which is very suitable for engineering applications based on chaos.

[1]  Fei Yu,et al.  Design and FPGA Implementation of a Pseudo-random Number Generator Based on a Hopfield Neural Network Under Electromagnetic Radiation , 2021, Frontiers in Physics.

[2]  Fei Yu,et al.  An Extremely Simple Multiwing Chaotic System: Dynamics Analysis, Encryption Application, and Hardware Implementation , 2021, IEEE Transactions on Industrial Electronics.

[3]  Huagan Wu,et al.  AC-induced coexisting asymmetric bursters in the improved Hindmarsh–Rose model , 2018 .

[4]  Jacques Kengne,et al.  A plethora of behaviors in a memristor based Hopfield neural networks (HNNs) , 2019 .

[5]  Chunhua Wang,et al.  A novel hyper-chaotic image encryption scheme based on quantum genetic algorithm and compressive sensing , 2020, Multimedia Tools and Applications.

[6]  Jacques Kengne,et al.  Complex dynamics of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight: Coexistence of multiple attractors and remerging Feigenbaum trees , 2018, AEU - International Journal of Electronics and Communications.

[7]  L. Chua.  Memristor-The missing circuit element , 1971 .

[8]  Yichuang Sun,et al.  Robust Multimode Function Synchronization of Memristive Neural Networks With Parameter Perturbations and Time-Varying Delays , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[9]  Jinde Cao,et al.  Hybrid multisynchronization of coupled multistable memristive neural networks with time delays , 2019, Neurocomputing.

[10]  Xiao-Song Yang,et al.  Chaos and transient chaos in simple Hopfield neural networks , 2005, Neurocomputing.

[11]  B. Bao,et al.  Bifurcation analysis and circuit implementation for a tabu learning neuron model , 2020 .

[12]  Tingwen Huang,et al.  Complex dynamical behavior of neural networks in circuit implementation , 2016, Neurocomputing.

[13]  Bocheng Bao,et al.  Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons , 2019, Nonlinear Dynamics.

[14]  Yichuang Sun,et al.  Synchronization of inertial memristive neural networks with time-varying delays via static or dynamic event-triggered control , 2020, Neurocomputing.

[15]  Yihua Hu,et al.  Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit , 2020 .

[16]  Yichuang Sun,et al.  Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations , 2020, Appl. Math. Comput..

[17]  Chunhua Wang,et al.  Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network , 2020, Appl. Math. Comput..

[18]  Hongmin Li,et al.  Image encryption algorithm with circle index table scrambling and partition diffusion , 2021, Nonlinear Dynamics.

[19]  Chunhua Wang,et al.  A Novel Hyperchaotic Image Encryption System Based on Particle Swarm Optimization Algorithm and Cellular Automata , 2021, Secur. Commun. Networks.

[20]  B. Eswara Reddy,et al.  Location Related Signals with Satellite Image Fusion Method Using Visual Image Integration Method , 2020, Comput. Syst. Sci. Eng..

[21]  Shenghong Huang,et al.  Application research of color design and collocation in image processing , 2020, Comput. Syst. Sci. Eng..

[22]  B. Kalaavathi,et al.  Adaptive Image Enhancement using Hybrid Particle Swarm Optimization and Watershed Segmentation , 2018 .

[23]  Kenli Li,et al.  A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function , 2019, Neurocomputing.

[24]  Zhen Wang,et al.  Chaos and hyperchaos in fractional-order cellular neural networks , 2012, Neurocomputing.

[25]  Sajad Jafari,et al.  Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow , 2019, Appl. Math. Comput..

[26]  Han Bao,et al.  Coexisting multiple firing patterns in two adjacent neurons coupled by memristive electromagnetic induction , 2018, Nonlinear Dynamics.

[27]  Feng Liu,et al.  A new chaotic Hopfield neural network and its synthesis via parameter switchings , 2013, Neurocomputing.

[28]  Chun-Lai Li,et al.  Image encryption scheme with bit-level scrambling and multiplication diffusion , 2021, Multimedia Tools and Applications.

[29]  Bocheng Bao,et al.  Two-neuron-based non-autonomous memristive Hopfield neural network: Numerical analyses and hardware experiments , 2018, AEU - International Journal of Electronics and Communications.

[30]  Zhigang Zeng,et al.  Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network , 2020, Nonlinear Dynamics.

[31]  Z. Zeng,et al.  Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications. , 2021, Chaos.

[32]  Xiao-Song Yang,et al.  Hyperchaos in Hopfield-type neural networks , 2005, Neurocomputing.

[33]  Kazuyuki Aihara,et al.  Bifurcation Analysis on Phase-Amplitude Cross-Frequency Coupling in Neural Networks with Dynamic Synapses , 2017, Front. Comput. Neurosci..

[34]  Feifei Yang,et al.  Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application , 2020 .

[35]  Hon Keung Kwan.  Simple sigmoid-like activation function suitable for digital hardware implementation , 1992 .

[36]  Nikolay V. Kuznetsov,et al.  Hidden chaotic sets in a Hopfield neural system , 2017 .

[37]  Xingyuan Wang,et al.  A color image encryption algorithm based on Hopfield chaotic neural network , 2019, Optics and Lasers in Engineering.

[38]  Yichuang Sun,et al.  Firing multistability in a locally active memristive neuron model , 2020, Nonlinear Dynamics.

[39]  Feng Ding,et al.  Digital Forensics for Recoloring via Convolutional Neural Network , 2020 .

[40]  Di Wang,et al.  LSTM Neural Network for Beat Classification in ECG Identity Recognition , 2019 .

[41]  Yichuang Sun,et al.  A Multi-Stable Memristor and its Application in a Neural Network , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[42]  Yong Chen,et al.  Effect of an autapse on the firing pattern transition in a bursting neuron , 2014, Commun. Nonlinear Sci. Numer. Simul..

[43]  Samira Pouyanfar,et al.  A Novel Combinational Convolutional Neural Network for Automatic Food-Ingredient Classification , 2020 .

[44]  Hairong Lin,et al.  Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation , 2020 .

[45]  Christos Volos,et al.  A novel memristive neural network with hidden attractors and its circuitry implementation , 2015, Science China Technological Sciences.

[46]  Fuad E. Alsaadi,et al.  A Hopfield neural network with multiple attractors and its FPGA design , 2018, The European Physical Journal Special Topics.

[47]  Min Long,et al.  Detecting Iris Liveness with Batch Normalized Convolutional Neural Network , 2019, Computers, Materials & Continua.

[48]  Xiaoxia Huang,et al.  Mean-semivariance models for fuzzy portfolio selection , 2008 .

[49]  Lingyun Xiang,et al.  An Encrypted Image Retrieval Method Based on SimHash in Cloud Computing , 2020 .

[50]  Feifei Yang,et al.  Dynamic characteristic of a new fractional-order chaotic system based on the Hopfield Neural Network and its digital circuit implementation , 2021, Physica Scripta.

[51]  Fei Yu,et al.  Chaos-Based Engineering Applications with a 6D Memristive Multistable Hyperchaotic System and a 2D SF-SIMM Hyperchaotic Map , 2021, Complex..

[52]  Ha Young Kim,et al.  Digital Vision Based Concrete Compressive Strength Evaluating Model using Deep Convolutional Neural Network , 2019, Computers, Materials & Continua.

[53]  Shuo Cai,et al.  Pseudorandom number generator based on a 5D hyperchaotic four-wing memristive system and its FPGA implementation , 2021, The European Physical Journal Special Topics.

[54]  Li Liu,et al.  Design and FPGA Implementation of a Pseudorandom Number Generator Based on a Four-Wing Memristive Hyperchaotic System and Bernoulli Map , 2019, IEEE Access.

[55]  Ge Zhang,et al.  A new neuron model under electromagnetic field , 2019, Appl. Math. Comput..

[56]  Xin Ge,et al.  Cryptanalysis and Improvement of a Chaotic Map-Control-Based and the Plain Image-Related Cryptosystem , 2019, Computers, Materials & Continua.

[57]  Jun Ma,et al.  Multiple modes of electrical activities in a new neuron model under electromagnetic radiation , 2016, Neurocomputing.

[58]  Huagan Wu,et al.  Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network , 2017 .

[59]  Shuo Cai,et al.  A new multi-scroll Chua's circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application , 2021, Integr..

[60]  Mo Chen,et al.  Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network , 2017, Front. Comput. Neurosci..

[61]  Junkang Ni,et al.  Chaotic dynamics in a neural network under electromagnetic radiation , 2018 .

[62]  Lihong Huang,et al.  Periodic attractor for reaction-diffusion high-order Hopfield neural networks with time-varying delays , 2017, Comput. Math. Appl..

[63]  Karthikeyan Rajagopal,et al.  Dynamical analysis, sliding mode synchronization of a fractional-order memristor Hopfield neural network with parameter uncertainties and its non-fractional-order FPGA implementation , 2019, The European Physical Journal Special Topics.

[64]  Chao Zhou,et al.  Neural Bursting and Synchronization Emulated by Neural Networks and Circuits , 2021, IEEE Transactions on Circuits and Systems I: Regular Papers.

[65]  Cong Xu,et al.  Image segmentation encryption algorithm with chaotic sequence generation participated by cipher and multi-feedback loops , 2021, Multimedia Tools and Applications.

[66]  Yichuang Sun,et al.  Weighted sum synchronization of memristive coupled neural networks , 2020, Neurocomputing.

[67]  Sajad Jafari,et al.  Chimera in a network of memristor-based Hopfield neural network , 2019, The European Physical Journal Special Topics.

[68]  Wei Yao,et al.  Chaotic dynamics in a neural network with different types of external stimuli , 2020, Commun. Nonlinear Sci. Numer. Simul..

[69]  Qingdu Li,et al.  On hyperchaos in a small memristive neural network , 2014 .

[70]  Chunhua Wang,et al.  A simple locally active memristor and its application in HR neurons. , 2020, Chaos.

[71]  Fei Yu,et al.  Pseudorandom Number Generator Based on Three Kinds of Four-Wing Memristive Hyperchaotic System and Its Application in Image Encryption , 2020, Complex..

[72]  S. Jafari,et al.  Firing patterns of an improved Izhikevich neuron model under the effect of electromagnetic induction and noise , 2020 .

[73]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[74]  Jing Liu,et al.  A Novel Robust Watermarking Algorithm for Encrypted Medical Image Based on DTCWT-DCT and Chaotic Map , 2019, Computers, Materials & Continua.