Investigation on the regular and chaotic dynamics of a ring network of five inertial Hopfield neural network: theoretical, analog and microcontroller simulation

Bao B et al (2023) Regime transition and multi-scroll hyperchaos in a discrete neuron model. Nonlinear Dyn 1–14

Bigelow TA (2020) Power and energy in electric circuits. In: Electric circuits, systems, and motors. Springer, Cham, pp 105–121

Boya BABF, Kengne J, Effa JY The effect of symmetry breaking in an inertial neural system with a non-monotonic activation function: theoretical study, asymmetric coexistence and experimental investigation. PHYSA-212639.

Cannas B, Cincotti S (2002) Hyperchaotic behaviour of two bi-directionally coupled Chua’s circuits. Int J Circuit Theory Appl 30(6):625–637

Article  Google Scholar 

Chedjou J et al (2001) Analog simulation of the dynamics of a van der Pol oscillator coupled to a Duffing oscillator. IEEE Trans Circuits Syst I Fundam Theory Appl 48(6):748–757

Article  Google Scholar 

Chen J et al. (2023) Scroll-growing/controlling chaotic attractors in cyclic Hopfield neural networks via memristive bridging. Physica Scr

Dana SK et al (2008) Multiscroll in coupled double scroll type oscillators. Int J Bifurc Chaos 18(10):2965–2980

Article  Google Scholar 

Doubla IS et al (2021) Multistability and circuit implementation of tabu learning two-neuron model: application to secure biomedical images in IoMT. Neural Comput Appl 33(21):14945–14973

Article  PubMed  PubMed Central  Google Scholar 

Doubla Isaac S, Njitacke ZT, Kengne J (2020) Effects of low and high neuron activation gradients on the dynamics of a simple 3D hopfield neural network. Int J Bifurc Chaos 30(11):2050159

Article  Google Scholar 

Fonzin Fozin T et al (2024) Superconductivity coupling of harmonic resonant oscillators: homogeneous and heterogeneous extreme multistability with multi-scrolls. Chaos Interdiscip J Nonlinear Sci 34(1):013148

Article  Google Scholar 

Foss J et al (1996) Multistability and delayed recurrent loops. Phys Rev Lett 76(4):708

Article  CAS  PubMed  Google Scholar 

Fu S et al (2023a) Multi-scroll Hopfield neural network under electromagnetic radiation and its brain-like coupling synchronization. Front Phys 11:1252568

Article  Google Scholar 

Fu S et al (2023b) Star memristive neural network: dynamics analysis, circuit implementation, and application in a color cryptosystem. Entropy 25(9):1261

Article  PubMed  PubMed Central  Google Scholar 

Kamdjeu Kengne L et al (2020) Dynamics, control and symmetry breaking aspects of a modified van der Pol-Duffing oscillator, and its analog circuit implementation. Analog Integr Circ Sig Process 103(1):73–93

Article  Google Scholar 

Kengne J et al (2016) Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit. Int J Bifurc Chaos 26(05):1650081

Article  Google Scholar 

Kengne J, Njikam S, Signing VF (2018) A plethora of coexisting strange attractors in a simple jerk system with hyperbolic tangent nonlinearity. Chaos Solitons Fractals 106:201–213

Article  Google Scholar 

Kengne J et al (2019) Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting. Chaos Solitons Fractals 121:63–84

Article  Google Scholar 

Krogh A (2008) What are artificial neural networks? Nat Biotechnol 26(2):195–197

Article  CAS  PubMed  Google Scholar 

Li F et al (2024) Cascade tri-neuron hopfield neural network: dynamical analysis and analog circuit implementation. AEU Int J Electron Commun 174:155037

Article  Google Scholar 

Lin H, Wang C, Tan Y (2020) Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation. Nonlinear Dyn 99(3):2369–2386

Article  Google Scholar 

Lin H et al (2022) Hyperchaotic memristive ring neural network and application in medical image encryption. Nonlinear Dyn 110(1):841–855

Article  Google Scholar 

Madasamy E et al (2023) Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation. Phys Scr 98(9):095219

Article  Google Scholar 

Maistrenko V, Sudakov O, Sliusar I (2021) Scroll ring chimera states in oscillatory networks. J Phys Commun 5(8):085001

Article  Google Scholar 

Majhi S et al (2019) Chimera states in neuronal networks: a review. Phys Life Rev 28:100–121

Article  PubMed  Google Scholar 

Mestl T, Lemay C, Glass L (1996) Chaos in high-dimensional neural and gene networks. Physica D 98(1):33–52

Article  Google Scholar 

Mostaghimi S et al (2019) Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow. Appl Math Comput 348:42–56

Google Scholar 

Njitacke ZT et al (2022a) Hamiltonian energy computation and complex behavior of a small heterogeneous network of three neurons: circuit implementation. Nonlinear Dyn 107(3):2867–2886

Article  Google Scholar 

Njitacke ZT et al (2022b) Complex dynamics and autapse-modulated information patterns in memristive Wilson neurons. Nonlinear Dyn 110(3):2793–2804

Article  Google Scholar 

Pisarchik AN, Hramov AE (2022) Multistability in Perception. Multistability in physical and living systems: characterization and applications. Springer, Berlin, pp 327–397

Chapter  Google Scholar 

Qi G, Hu J (2020) Modelling of both energy and volume conservative chaotic systems and their mechanism analyses. Commun Nonlinear Sci Numer Simul 84:105171

Article  Google Scholar 

Qi G, Liang X (2017) Mechanism and energy cycling of the Qi four-wing chaotic system. Int J Bifurc Chaos 27(12):1750180

Article  Google Scholar 

Qi G, Zhang J (2017) Energy cycle and bound of Qi chaotic system. Chaos Solitons Fractals 99:7–15

Article  Google Scholar 

Ramadoss J et al (2022) Multiple Hopf bifurcations, period-doubling reversals and coexisting attractors for a novel chaotic jerk system with Tchebytchev polynomials. Physica A 587:126501

Article  Google Scholar 

Ramshaw R, Schuurman D (1997) PSPICE Simulation of power electronics circuits. Chapman & Hall, London

Google Scholar 

Song Z, Xu J, Zhen B (2019) Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function. Math Biosci Eng 16(6):6406–6426

Article  PubMed  Google Scholar 

Sriram S et al (2022) Coexistence of multiscroll chaotic attractors in two coupled inertial hopfield neurons: numerical simulations and experiment. Phys Scr 97(12):125207

Article  CAS  Google Scholar 

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

Book  Google Scholar 

Sundarambal B et al (2023) Theoretical study and circuit implementation of three chain-coupled self-driven Duffing oscillators. Chaos Interdiscip J Nonlinear Sci 33(11):113134

Article  Google Scholar 

Sussillo D, Barak O (2013) Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural Comput 25(3):626–649

Article  PubMed  Google Scholar 

Tanekou ST et al (2023) Coexistence of periodic, chaotic and hyperchaotic attractors in a system consisting of a duffing oscillator coupled to a van der Pol oscillator. Int J Bifurc Chaos 33(02):2330004

Article  Google Scholar 

Tripathi BK, Kalra PK (2010) High dimensional neural networks and applications. Intelligent autonomous systems: foundations and applications. Springer, pp 215–233

Chapter  Google Scholar 

Tsafack N, Kengne J (2019) Complex dynamics of the Chua’s circuit system with adjustable symmetry and nonlinearity: multistability and simple circuit realization. World J Appl Phys 4(2):24

Article  Google Scholar 

Upadhyay RK (2003) Multiple attractors and crisis route to chaos in a model food-chain. Chaos Solitons Fractals 16(5):737–747

Article  Google Scholar 

Wang Z, Wang R (2014) Energy distribution property and energy coding of a structural neural network. Front Comput Neurosci 8:14

Article  PubMed  PubMed Central  Google Scholar 

Wang J et al (2021) Fractional-order analysis of modified Chua’s circuit system with the smooth degree of 3 and its microcontroller-based implementation with analog circuit design. Symmetry 13(2):340

Article  Google Scholar 

Wang C et al (2024) High-dimensional memristive neural network and its application in commercial data encryption communication. Expert Syst Appl 242:122513

Article  CAS  Google Scholar 

Wolf A et al (1985) Determining Lyapunov exponents from a time series. Physica D 16(3):285–317

Article  Google Scholar 

Yanchuk S, Kapitaniak T (2001) Symmetry-increasing bifurcation as a predictor of a chaos-hyperchaos transition in coupled systems. Phys Rev E 64(5):056235

Article  CAS 

Comments (0)

No login
gif