Berger DL, De Arcangelis L, Herrmann HJ (2017) Spatial features of synaptic adaptation affecting learning performance. Sci Rep 7(1):11016

Article  PubMed  PubMed Central  Google Scholar 

Bao B, Hou L, Zhu Y, Wu H, Chen M (2020) Bifurcation analysis and circuit implementation for a tabu learning neuron model. AEU-Int J Electron Commun 121:153235

Article  Google Scholar 

Bao H, Liu W, Hu A (2019) Coexisting multiple firing patterns in two adjacent neurons coupled by memristive electromagnetic induction. Nonlinear Dyn 95:43–56

Article  Google Scholar 

Bahramian A, Parastesh F, Pham V-T, Kapitaniak T, Jafari S, Perc M (2021) Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net. Chaos Interdiscip J Nonlinear Sci 31(3)

Bao H, Yu X, Xu Q, Wu H, Bao B (2023) Three-dimensional memristive Morris–Lecar model with magnetic induction effects and its FPGA implementation. Cogn Neurodyn 17(4):1079–1092

Article  PubMed  Google Scholar 

Bao B, Zhu Y, Li C, Bao H, Xu Q (2020) Global multistability and analog circuit implementation of an adapting synapse-based neuron model. Nonlinear Dyn 101(2):1105–1118

Article  Google Scholar 

Bao B, Zhu Y, Ma J, Bao H, Wu H, Chen M (2021) Memristive neuron model with an adapting synapse and its hardware experiments. Sci China Technol Sci 64(5):1107–1117

Article  Google Scholar 

Bao H, Zhang J, Wang N, Kuznetsov N, Bao B (2022) Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins. Chaos Interdiscip J Nonlinear Sci 32(12)

Chay TR (1985) Chaos in a three-variable model of an excitable cell. Physica D 16(2):233–242

Article  Google Scholar 

Chen J, Li C-G (2011) Chaos in a neuron model with adaptive feedback synapse: electronic circuit design. Acta Phys Sin 60(5):050503

Article  Google Scholar 

Datseris G (2018) Dynamicalsystems.jl: A julia software library for chaos and nonlinear dynamics. J Open Source Softw 3(23):598. https://doi.org/10.21105/joss.00598

Dong DW, Hopfield JJ (1992) Dynamic properties of neural networks with adapting synapses. Netw Comput Neural Syst 3(3):267

Ding S, Wang N, Bao H, Chen B, Wu H, Xu Q (2023) Memristor synapse-coupled piecewise-linear simplified hopfield neural network: Dynamics analysis and circuit implementation. Chaos Soliton Fract 166:112899

Article  Google Scholar 

Eftekhari L, Amirian MM (2023) Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure. Cogn Neurodyn 17(4):1045–1059

Article  PubMed  Google Scholar 

Eckmann J-P, Kamphorst SO, Ruelle D (1995) Recurrence plots of dynamical systems. World Sci Ser Nonlinear Sci Ser A 16:441–446

Google Scholar 

FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1(6):445–466

Article  PubMed  PubMed Central  CAS  Google Scholar 

Ghosh D, Frasca M, Rizzo A, Majhi S, Rakshit S, Alfaro-Bittner K, Boccaletti S (2022) The synchronized dynamics of time-varying networks. Phys Rep 949:1–63

Article  Google Scholar 

Gao X, Mou J, Banerjee S, Zhang Y (2023) Color-gray multi-image hybrid compression-encryption scheme based on BP neural network and knight tour. IEEE Trans Cybernet 53(8):5037–5047

Article  Google Scholar 

Gu H, Pan B, Chen G, Duan L (2014) Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dyn 78(1):391–407

Article  Google Scholar 

Hodgkin A, Huxley A (1990) A quantitative description of membrane current and its application to conduction and excitation in nerve. Bull Math Biol 52:25–71

Article  PubMed  CAS  Google Scholar 

Hou B, Hu X, Guo Y, Ma J (2023) Energy flow and stochastic resonance in a memristive neuron. Phys Scr 98(10):105236

Article  CAS  Google Scholar 

Hajian DN, Ramadoss J, Natiq H, Parastesh F, Rajagopal K, Jafari S (2023) Dynamics of Hindmarsh–Rose neurons connected via adaptive memristive synapse. Chin J Phys

Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J (2004) Phase synchronization in ensembles of bursting oscillators. Phys Rev Lett 93(13):134101

Article  PubMed  Google Scholar 

Joseph D, Ramachandran R, Karthikeyan A, Rajagopal K (2023) Synchronization studies of Hindmarsh–Rose neuron networks: unraveling the influence of connection induced memristive synapse. Biosystems 234:105069

Article  PubMed  CAS  Google Scholar 

Kumarasamy S, Moroz IM, Sampathkumar SK, Karthikeyan A, Rajagopal K (2023) Dynamics and network behavior of a four-dimensional discrete neuron model with magnetic flux coupling. Eur Phys J Plus 138(8):683

Article  Google Scholar 

Kuramoto Y (2012) Chaos and statistical methods. In: Proceedings of the Sixth Kyoto Summer Institute, Kyoto, Japan September 12–15, 1983 vol. 24. Springer, New York

Kong X, Yu F, Yao W, Cai S, Zhang J, Lin H (2024) Memristor-induced hyperchaos, multiscroll and extreme multistability in fractional-order HNN: image encryption and FPGA implementation. Neural Netw 171:85–103

Article  PubMed  Google Scholar 

Li C, Chen G (2005) Coexisting chaotic attractors in a single neuron model with adapting feedback synapse. Chaos Soliton Fract 23(5):1599–1604

Article  Google Scholar 

Liu Z, Wang C, Jin W, Ma J (2019) Capacitor coupling induces synchronization between neural circuits. Nonlinear Dyn 97:2661–2673

Article  Google Scholar 

Lv M, Wang C, Ren G, Ma J, Song X (2016) Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn 85:1479–1490

Article  Google Scholar 

Li T, Yu D, Wu Y, Ding Q, Jia Y (2024) Stochastic resonance in the small-world networks with higher order neural motifs interactions. Eur Phys J Spec Top 1–10

Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1):193–213

Article  PubMed  PubMed Central  CAS  Google Scholar 

Marwan N, Romano MC, Thiel M, Kurths J (2007) Recurrence plots for the analysis of complex systems. Phys Rep 438(5–6):237–329

Article  Google Scholar 

Pal K, Ghosh D, Gangopadhyay G (2021) Synchronization and metabolic energy consumption in stochastic Hodgkin-Huxley neurons: patch size and drug blockers. Neurocomputing 422:222–234

Article  Google Scholar 

Parastesh F, Rajagopal K, Jafari S, Perc M, Schöll E (2022) Blinking coupling enhances network synchronization. Phys Rev E 105(5):054304

Article  PubMed  CAS  Google Scholar 

Ramasamy M, Kumarasamy S, Sampathkumar SK, Karthikeyan A, Rajagopal K, et al (2023) Synchronizability of discrete nonlinear systems: a master stability function approach. Complexity 2023

Riecke H, Roxin A, Madruga S, Solla SA (2007) Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons. Chaos Interdiscip J Nonlinear Sci 17(2)

Sharma A (2019) Explosive synchronization through dynamical environment. Phys Lett A 383(17):2051–2055

Article  CAS  Google Scholar 

Sun J, Li C, Wang Z, Wang Y (2023) A memristive fully connect neural network and application of medical image encryption based on central diffusion algorithm. IEEE Trans Ind Inform

Sugase-Miyamoto Y, Liu Z, Wiener MC, Optican LM, Richmond BJ (2008) Short-term memory trace in rapidly adapting synapses of inferior temporal cortex. PLoS Comput Biol 4(5):1000073

Article  Google Scholar 

Strogatz SH (2018) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. CRC Press

Usha K, Subha P (2019) Hindmarsh–Rose neuron model with memristors. Biosystems 178:1–9

Article  Google Scholar 

Wang Z, Chen Z, Wang Y, Sun J (2023) Application of chaotic systems reduced-order observer synchronization based on DNA strand displacement in information encryption of the IoT. IEEE Internet Things J

Wu F, Guo Y, Ma J (2023) Energy flow accounts for the adaptive property of functional synapses. Sci China Technol Sci 66(11):3139–3152

Article  CAS  Google Scholar 

Wang G, Jin W, Wang A (2015) Synchronous firing patterns and transitions in small-world neuronal network. Nonlinear Dyn 81(3):1453–1458

Article  Google Scholar 

Wang Q, Perc M, Duan Z, Chen G (2010) Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling. Physica A 389(16):3299–3306

Article  Google Scholar 

Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442

Article  PubMed  CAS  Google Scholar 

Wang G, Yu D, Ding Q, Li T, Jia Y (2021) Effects of electric field on multiple vibrational resonances in Hindmarsh–Rose neuronal systems. Chaos Soliton Fract 150:111210

Article  Google Scholar 

Xu Q, Ding S, Bao H, Chen M, Bao B (2021) Piecewise-linear simplification for adaptive synaptic neuron model. IEEE Trans Circuits Syst II Express Briefs 69(3):1832–1836

Google Scholar 

Xu Q, Liu T, Ding S, Bao H, Li Z, Chen B (2023) Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction. Cogn Neurodyn 17(3):755–766

Article  PubMed  Google Scholar 

Xu Q, Tan X, Zhu D, Bao H, Hu Y, Bao B (2020) Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit. Chaos Soliton Fract 141:110353