| Citation: |
Xueying Shi, Xiaoping Chen, Chengdai Huang. DELAY-INDUCED HOPF BIFURCATION OF A FRACTIONAL-ORDER NEURAL NETWORK WITH BOTH NEUTRAL AND INERTIAL TERMS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 362-379. doi: 10.11948/20250068
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DELAY-INDUCED HOPF BIFURCATION OF A FRACTIONAL-ORDER NEURAL NETWORK WITH BOTH NEUTRAL AND INERTIAL TERMS
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Abstract
This paper focuses on the stability and bifurcation in a fractional-order neutral-type inertial neural network with time delay. We mainly analyze the new system with time delay by using Cramer's rule to derive precise bifurcation conditions. The accuracy of the theoretical findings is ultimately confirmed through two numerical experiments. Moreover, the remarkable advantages of the fractional-order model are found in delaying the occurrence of inherent bifurcations and enhancing the stability performance.
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Keywords:
- Fractional-order /
- neural networks /
- stability /
- Hopf bifurcation /
- neutral and inertial terms
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References
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Xueying Shi, Xiaoping Chen, Chengdai Huang. DELAY-INDUCED HOPF BIFURCATION OF A FRACTIONAL-ORDER NEURAL NETWORK WITH BOTH NEUTRAL AND INERTIAL TERMS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 362-379. doi: 10.11948/20250068
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Figure 1.
The waveform diagrams of system (5.1) with
$ \varsigma=0.85<\varsigma_0=0.9733 $ -
Figure 2.
The phase diagrams of system (5.1) with
$ \varsigma=0.85<\varsigma_0=0.9733 $ -
Figure 3.
The waveform diagrams of system (5.1) with
$ \varsigma=1.1>\varsigma_0=0.9733 $ -
Figure 4.
The phase diagrams of system (5.1) with
$ \varsigma=1.1>\varsigma_0=0.9733 $ -
Figure 5.
Influence of
$ h_i $ $ \varsigma_0 $ -
Figure 6.
Comparison on the stability of system (5.1) in integer-order and fractional-order.
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Figure 7.
Comparison on the stability of system (5.1) in integer-order and fractional-order.
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Figure 8.
Comparison on the stability of system (5.1) in integer-order and fractional-order.
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Figure 9.
Comparison on the stability of system (5.1) in integer-order and fractional-order.
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Figure 10.
The waveform diagrams of system (5.2) with
$ \varsigma=0.65<\varsigma_0=0.8025 $ -
Figure 11.
The phase diagrams of system (5.2) with
$ \varsigma=0.65<\varsigma_0=0.8025 $ -
Figure 12.
The waveform diagrams of system (5.2) with
$ \varsigma=0.9<\varsigma_0=0.8025 $ -
Figure 13.
The phase diagrams of system (5.2) with
$ \varsigma=0.9>\varsigma_0=0.8025 $ -
Figure 14.
Influence of
$ h_i $ $ \varsigma_0 $ -
Figure 15.
Comparison on the stability of system (5.2) in integer-order and fractional-order.
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Figure 16.
Comparison on the stability of system (5.2) in integer-order and fractional-order.
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Figure 17.
Comparison on the stability of system (5.2) in integer-order and fractional-order.
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Figure 18.
Comparison on the stability of system (5.2) in integer-order and fractional-order.