On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment

Hu, Haijun; Tao, Yi; Zou, Xingfu

doi:10.1090/proc/14659

Cited by 76 publications

(22 citation statements)

References 11 publications

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“…In the future, we shall further improve NTCTZNN by introducing triple integrals to enhance its robustness to quadratic noise and study delayed ZNNs based on the theoretical results obtained in [23][24][25][26][27][28].…”

Section: Discussionmentioning

confidence: 99%

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

Sun

Liu

2020

Adv Differ Equ

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The Zhang neural network (ZNN) has become a benchmark solver for various time-varying problems solving. In this paper, leveraging a novel design formula, a noise-tolerant continuous-time ZNN (NTCTZNN) model is deliberately developed and analyzed for a time-varying Lyapunov equation, which inherits the exponential convergence rate of the classical CTZNN in a noiseless environment. Theoretical results show that for a time-varying Lyapunov equation with constant noise or time-varying linear noise, the proposed NTCTZNN model is convergent, no matter how large the noise is. For a time-varying Lyapunov equation with quadratic noise, the proposed NTCTZNN model converges to a constant which is reciprocal to the design parameter. These results indicate that the proposed NTCTZNN model has a stronger anti-noise capability than the traditional CTZNN. Beyond that, for potential digital hardware realization, the discrete-time version of the NTCTZNN model (NTDTZNN) is proposed on the basis of the Euler forward difference. Lastly, the efficacy and accuracy of the proposed NTCTZNN and NTDTZNN models are illustrated by some numerical examples.

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Section: Discussionmentioning

confidence: 99%

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

Sun

Liu

2020

Adv Differ Equ

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“…and conditions (7), (8), and (28) of Theorem 3.3 hold. Then system (1) and the isolated networks (2) with continuous activations are finite-time synchronized under the following adaptive feedback control protocol:…”

Section: Corollary 34 Suppose That Assumption [H 4 ]mentioning

confidence: 94%

“…In recent times, differential equation and fractional differential equation models have found their applications in a variety of fields including biology [1][2][3][4][5][6], physics [7][8][9][10], engineering [11][12][13][14], mathematics [15][16][17][18], information technology, and so on [19][20][21][22][23][24][25][26][27]. They are also one of the most rudimentary tools for neural networks.…”

Section: Introduction and Modelingmentioning

confidence: 99%

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

et al. 2020

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In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.

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“…Remark To the author's knowledge, the issue of antiperiodic RNNs involving proportional delays has never been investigated. Obviously, the corresponding conclusions in Shao, Tan, Gong, Cao, Li, Zhou, Yang, Wang, Peng and Wang, Cai et al, Li et al, Kudu, Hu et al, Hu and Zou, Huang et al, and Hu et al and the references cited therein cannot be used to deal with the exponential convergence on the

π

antiperiodic phenomenon for system .…”

Section: Numerical Example and Simulationsmentioning

confidence: 99%

Stability of antiperiodic recurrent neural networks with multiproportional delays

Huang

Long

Cao

2020

Math Methods in App Sciences

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In general, a proportional function is obviously not antiperiodic, yet a very interesting fact in this paper shows that it is possible there is an antiperiodic solution for some proportional delayed dynamical systems. We deal with the issue of antiperiodic solutions for RNNs (recurrent neural networks) incorporating multiproportional delays. Employing Lyapunov method, inequality techniques and concise mathematical analysis proof, sufficient criteria on the existence of antiperiodic solutions including its uniqueness and exponential stability are built up. The obtained results provide us some lights for designing a stable RNNs and complement some earlier publications. In addition, simulations show that the theoretical antiperiodic dynamics are in excellent agreement with the numerically observed behavior. KEYWORDSantiperiodic, proportional delay, recurrent neural network, stability MSC CLASSIFICATION 34C25; 34K13; 34K25Math Meth Appl Sci. 2020;43:6093-6102.wileyonlinelibrary.com/journal/mma

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On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment

Cited by 76 publications

References 11 publications

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

Stability of antiperiodic recurrent neural networks with multiproportional delays

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