Energy balance and synchronization via inductive-coupling in functional neural circuits

Xie, Ying; Zhou, Ping; Ma, Jun

doi:10.1016/j.apm.2022.09.015

Cited by 57 publications

(6 citation statements)

References 70 publications

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“…Calculating the Hamilton energy of memristive circuits helps to understand the oscillatory characteristics, and by analyzing the variation of the Hamilton energy one can understand the operating state and performance of the memristive circuit. According to the Helmholtz theorem [45,46], the Hamilton vector field of the model can be written as…”

Section: The Model Of Memristive Mapmentioning

confidence: 99%

Dynamical analysis of a new memristive map with offset boosting and extreme multistability

Han,

Cao,

et al. 2024

Phys. Scr.

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In this paper, a memristive circuit is designed based on a charge-controlled memristor, and the Hamilton energy function is obtained from the Helmholtz theorem. The system equation of memristive circuit is discretized by redefining the variables to obtain a three-dimensional memristive map and the corresponding energy function. Then, the effects of parameters and initial values on the memristive map are analyzed using conventional dynamical analysis. There are multiple types of quasi-periodic and chaotic states of the memristive map under different parameters, and the energy evolution of different states is shown. In addition, offset boosting and homogeneous extreme multistability are found in the map, which can be controlled to offset the attractor by changing specific parameters and initial values. The complexity of the chaotic sequence is also analyzed as the parameters and initial values are varied over the chosen range. Finally, the map is implemented on PSIM circuit simulation and digital signal processor (DSP) respectively. This research will provide a reference for secure communication.

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Section: The Model Of Memristive Mapmentioning

confidence: 99%

Dynamical analysis of a new memristive map with offset boosting and extreme multistability

Han,

Cao,

et al. 2024

Phys. Scr.

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“… If the drive system and response system are connected with a resistor and capacitor in parallel, the control synchronization of simplest Chua's circuits via linear and nonlinear channels can be studied [22,23]. Figure 3 is the schematic diagram of two simplest Chua's chaotic circuits coupled system.…”

Section: Synchronization Of Two Simplest Chua's Chaotic Circuitsmentioning

confidence: 99%

“…Chaotic synchronization is an important research subject in chaos. Chaos synchronization, in which two or more chaotic systems finally reach state consistency under different initial states by internal coupling action or external input control, has attracted plenty of researchers' attention for its applications in synchronous control, secure communication, image encryption, and neural networks, etc [20][21][22][23][24][25][26][27]. Bao et al presented a simple 2D sine map suitable for synchronously output multichannel initial-controlled chaotic sequences [28].…”

Section: Introductionmentioning

confidence: 99%

Control synchronization of Chua's circuits via linear and nonlinear channels

Hu,

Yang,

Zhu

et al. 2023

Phys. Scr.

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Synchronization plays an important role in regulating coupled chaotic systems. In this paper, capacitor-based field coupling and resistive coupling are applied to tame a class of chaotic circuits, stability analysis, and circuit verification in Multisim are carried out. Synchronization of two and three coupled Chua’s circuits can be reached via linear and nonlinear channels by resistor and capacitor connection in parallel. The range of synchronous coupling resistance R cp approximately decreases with coupling capacitance C cp increasing in the two circuits coupled system. In the three circuits coupled system, the range of synchronous coupling resistance R 12 decreases with the increase of another coupling resistance R 23. Compared with two circuits coupled system, the implementation of the synchronization process takes longer in three circuits coupled system with the same parameters. In addition, the three non-identical circuits coupled system is studied. Indirect coupling synchronization between driving and response systems without directly coupling can be achieved via an asynchronous intermediate system. Its application in chaotic, secure communication is discussed.

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“…According to the Helmholtz theorem, relationships between firing patterns and energy are found by using numerical computation methods. [27][28][29][30][31][32] The energy consumption of the Hindmarsh-Rose neuron during its signaling activity can be evaluated by calculating the energy function. [33] The neural networks based on the different neurons can show collective behavior and functional properties.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and synchronization of neural models with memristive membranes under energy coupling

Wan 万,

Wu 吴,

Ma 马

et al. 2024

Chinese Phys. B

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Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms. The electrophysiological environment inside and outside of the nerve cell is different. Given the continuous and periodical properties of electromagnetic fields in the cell during its working, electronic components involving two capacitors and a memristor are effective in mimicking the physical features. In this paper, a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance. It is found that the memristive neural circuit can present abundant firing patterns without stimulus. The Hamilton energy function is deduced by using the Helmholtz theorem. Further, the neuronal network consisting of memristive neurons is proposed by introducing energy coupling. The controllability and flexibility of parameters make the model have the ability to describe the dynamics and synchronization behaviors.

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Energy balance and synchronization via inductive-coupling in functional neural circuits

Cited by 57 publications

References 70 publications

Dynamical analysis of a new memristive map with offset boosting and extreme multistability

Dynamical analysis of a new memristive map with offset boosting and extreme multistability

Control synchronization of Chua's circuits via linear and nonlinear channels

Dynamics and synchronization of neural models with memristive membranes under energy coupling

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