Dynamic Analysis and Synchronization Control of Extremely Simple Cyclic Memristive Chaotic Neural Network

LAI Qiang; QIN Minghong

doi:10.11999/JEIT250212

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LAI Qiang, QIN Minghong. Dynamic Analysis and Synchronization Control of Extremely Simple Cyclic Memristive Chaotic Neural Network[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250212

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LAI Qiang, QIN Minghong. Dynamic Analysis and Synchronization Control of Extremely Simple Cyclic Memristive Chaotic Neural Network[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250212

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Dynamic Analysis and Synchronization Control of Extremely Simple Cyclic Memristive Chaotic Neural Network

doi: 10.11999/JEIT250212 cstr: 32379.14.JEIT250212

LAI Qiang^,,
QIN Minghong

School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China

Funds: The National Natural Science Foundation of China (62366014)

Received Date: 2025-03-31
Rev Recd Date: 2025-07-02

Available Online: 2027-07-09

Abstract

Abstract

Objective Memristors are considered promising devices for the construction of artificial synapses because their unique nonlinear and non-volatile properties effectively mimic the functions and mechanisms of biological synapses. These features have made memristors a research focus in brain-inspired science. Memristive neural networks, composed of memristive neurons or memristive synapses, constitute a class of biomimetic artificial neural networks that exhibit dynamic behaviors more closely aligned with those of biological neural systems and provide more plausible biological interpretations. Since the concept of the memristive neural network was proposed, extensive pioneering research has been conducted, revealing several critical issues that require further exploration. Although current memristive neural networks can generate complex dynamic behaviors such as chaos and multistability, these effects are often achieved at the cost of increased network complexity or the requirement for specialized memristive characteristics. Therefore, the systematic exploration of simple memristive neural networks that can produce diverse dynamic behaviors, the proposal of practical design strategies, and the development of efficient, precise control schemes remain of considerable research value. Methods This paper proposes a chaoticization method for an Extremely Simple Cyclic Memristive Convolutional Neural Network (ESCMCNN) that contains only unidirectional synaptic connections based on memristors. Using a three-node neural network as an example, a class of memristive cyclic neural networks with simple structures and rich dynamic behaviors is constructed. Numerical analysis tools, including bifurcation diagrams, basins of attraction, phase plane diagrams, and Lyapunov exponents, are employed to investigate the networks’ diverse bifurcation processes, multiple types of multistability, and multi-variable signal amplitude control. Electronic circuit experiments are used to validate the feasibility of the proposed networks. Finally, a novel multi-power reaching law is developed to achieve chaotic synchronization within fixed time. Results and Discussions For a three-node cyclic neural network initially in a periodic state, two network chaotification methods—full-synaptic memristivation and multi-node extension—are proposed using magnetically controlled memristors (Fig. 1). Phase plane diagrams illustrate the chaotic attractors generated by these networks (Fig. 2), confirming the feasibility of the proposed methods. Using network (B) as an example, numerical analysis tools are utilized to study its diverse dynamic evolution processes (Fig. 5, Fig. 6, Fig. 7), various forms of multistability (Fig. 8, Fig. 9), and multi-variable amplitude control (Fig. 10). The physical realization of network (B) is further demonstrated through circuit experiments (Fig. 11, Fig. 12). Additionally, the effectiveness of the fixed-time synchronization control strategy for network (B) is verified through numerical simulations (Fig. 13, Fig. 14). Conclusions This paper proposes a construction method for the ESCMCNN capable of generating rich dynamic behaviors. A series of ESCMCNNs is successfully designed based on a three-node neural network in a periodic state. The dynamic evolution of the ESCMCNN as a function of memristive parameters is investigated using numerical tools, including single- and dual-parameter bifurcation diagrams and Lyapunov exponents. Under different initial conditions, the ESCMCNN exhibits various forms of multistability, including the coexistence of point attractors with periodic attractors, and point attractors with chaotic attractors. The study further demonstrates that the oscillation amplitudes of multiple variables in the ESCMCNN are strongly dependent on the memristive coupling strength. The reliability of these numerical results is confirmed through electronic circuit experiments. In addition, a novel multi-power reaching law is proposed to achieve fixed-time synchronization of the network, and its feasibility and effectiveness are validated through simulation tests.
- Memristive neural network,
- Multistability,
- Dynamic analysis,
- Fixed-time synchronization

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References(21)

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