Heterogeneous Coexisting Attractors, Large-scale Amplitude Control, and Finite-time Synchronization of Central Cyclic Memristive Neural Networks

Information Science Artificial Intelligence Electromagnetism Physics
chaos memristor memristive neural networks heterogeneous coexisting attractors large-scale amplitude control finite-time synchronization

Heterogeneous Coexisting Attractors, Large-Scale Amplitude Control and Finite-Time Synchronization of Central Cyclic Memristive Neural Networks

Academic Background

Due to their memory and nonlinearity characteristics similar to brain synapses, memristors hold significant theoretical and practical importance in the study of chaotic dynamics in brain-like neural networks. With the development of big data and artificial intelligence in recent years, the limitations of traditional fixed neural network models in mapping brain structure and function have gradually become apparent. This has become a major obstacle to further advancements in morphological neurology research. Since HP Labs first developed the physical nonlinear memristor in 2008, memristors have garnered widespread attention in the field of artificial neural networks. Constructing memristive neural networks (MNNs) is extremely important for studying the relationship between brain structure and function, analyzing neural system mechanisms, enhancing artificial intelligence decision-making, optimizing adaptive control, and accelerating hardware computation.

Paper Source

This paper, “Heterogeneous Coexisting Attractors, Large-Scale Amplitude Control and Finite-Time Synchronization of Central Cyclic Memristive Neural Networks,” was authored by Qiang Lai and Shicong Guo from the School of Electrical and Automation Engineering at East China Jiaotong University. The paper will be published in the journal Neural Networks and was accepted on May 26, 2024.

Research Process

  1. Model Construction and Numerical Verification

    • This study introduced a self-feedback memristor into a four-dimensional Hopfield Neural Network (HNN) to construct a Central Cyclic Memristive Neural Network (CCMNN).
    • By simulating neural synapses using a hyperbolic memristor, a mathematical model of an HNN containing four neurons was constructed, followed by equilibrium point analysis and stability analysis.
    • Through equilibrium point stability analysis and numerical simulations of phase diagrams, bifurcation diagrams, time-domain diagrams, and Lyapunov Exponents (LEs), it was found that the CCMNN exhibits multi-stable coexistence behavior under different initial conditions, such as period-period, period-stability point, period-chaos, and stability point-chaos coexisting phenomena.

  2. Study of Complex Dynamic Behavior

    • An in-depth study of the variations in the internal parameters of the CCMNN revealed the diversity and complexity of chaotic, bifurcation, isomorphic coexisting attractors, and heterogeneous coexisting attractors.
    • By calculating the Lyapunov Exponents, it was determined whether the system exhibits chaotic behavior, which was highly consistent with the bifurcation diagram. The system transitions between periodic and chaotic states as parameter c changes.

  3. Large-Scale Amplitude Control

    • The study showed that by adjusting structural parameters, large-scale amplitude control of state variables can be achieved without changing the chaotic state of the system. This feature provides an effective method for amplitude control in dynamic behavior.

  4. Synchronization Control and Application

    • An adaptive control method was used to construct a synchronization controller, aiming to achieve finite-time synchronization control of the CCMNN and explore its potential application in simple secure communication.
    • Theoretical proofs and numerical simulations validated the feasibility and effectiveness of the synchronization scheme. By selecting appropriate parameters and designing corresponding controllers, master networks and slave networks can be quickly synchronized, causing system errors to converge to zero.

  5. Secure Communication Implementation

    • In secure communication, chaos masking technology was used to encrypt and decrypt information via the CCMNN. The information signal was encrypted into a chaotic mask signal at the sender’s end and decrypted by a matching response network at the receiver’s end to restore the original signal.
    • Simulations validated that this design could effectively encrypt and decrypt information, demonstrating high adaptability and security.

  6. NIST Test Validation

    • To verify the security and reliability of the CCMNN in practical applications, systematic random tests were conducted using the National Institute of Standards and Technology (NIST) suite.
    • The results showed that the pseudo-random numbers generated by the CCMNN passed various NIST tests, confirming their high randomness and security.

Research Results

  • Diverse Dynamic Behavior: The study revealed various complex dynamic behaviors of the CCMNN under different parameter settings, including isomorphic coexisting attractors, heterogeneous coexisting attractors, large-scale chaos, and amplitude control.
  • Adaptive Synchronization Control: An adaptive control method was designed, successfully achieving finite-time synchronization of the CCMNN, ensuring the system reaches stability quickly during the synchronization process.
  • Secure Communication System: Applications of the CCMNN in simple secure communication were experimented with, proving that through chaos masking technology, effective encryption and decryption of information could be achieved.
  • NIST Test Validation: The study validated the high randomness and security of the generated pseudo-random numbers through NIST random tests, further proving the potential application value of the CCMNN in information encryption.

Conclusion

This study demonstrates the immense potential of memristive neural networks in complex dynamic behaviors, large-scale amplitude control, and secure communication. By deeply exploring the dynamic characteristics of the CCMNN, new avenues for analyzing neural system mechanisms in the human brain have been provided, along with new possibilities for realizing next-generation computing architectures and various other applications. Particularly in the realm of secure communication, the study shows that memristive neural networks have significant application value in enhancing the security and reliability of information transmission.

Through this research, the academic community has not only gained a deeper understanding of the application of memristors in chaotic dynamics and neural networks but also laid a solid foundation and direction for further research in artificial intelligence and neuroscience.