This paper presents a class of high-order cellular neural networks (HCNNs) with mixed discontinuous activations and time-varying leakage delays. To deal with the discontinuous property, the framework of Filippov solution is invoked to solve the inexistence of the classical solutions. Then combining with the functional differential inclusions theory and inequality technique, some new verifiable algebraic criteria are given to ensure that all solutions of the proposed neural network converge exponentially to the zero vector. The results obtained in this paper not only extend earlier works on HCNNs to the discontinuous case but also complement the previous researches on discontinuous neural networks since the mixed discontinuous activations have never been touched. Consequently, the results we established are more generalized. Finally, the effectiveness of the obtained results are illustrated via numerical examples and simulations.
- Open Access
- Article
New Results on Global Exponential Convergence of Discontinuous HCNNs with Time-Varying Leakage Delays
- Yi Xia,
- Na Zhao *
Author Information
Received: 25 Jan 2026 | Revised: 17 Mar 2026 | Accepted: 29 Apr 2026 | Published: 07 May 2026
Abstract
Keywords
high-order cellular neural network | discontinuous activations | time-varying leakage delays | exponential convergence
References
- 1.
Dembo, A.; Farotimi, O.; Kailath, T. High-order absolutely stable neural networks. IEEE Trans. Circuits Syst. 1991, 38, 57–65.
- 2.
Liu, X.J. Improved convergence criteria for HCNNs with delays and oscillating coefficients in leakage terms. Neural Comput. Appl. 2016, 27, 917–925.
- 3.
Xu, Y. Anti-periodic solutions for HCNNs with time-varying delays in the leakage terms. Neural Comput. Appl. 2014, 24, 1047–1058.
- 4.
Xiong, W.M. New result on convergence for HCNNs with time-varying leakage delays. Neural Comput. Appl. 2015, 26, 485–491.
- 5.
Xu, Y.; Zhong, J. Convergence of neutral type proportional-delayed HCNNs with D operators. Int. J. Biomath. 2019, 12, 1950002.
- 6.
Yu, Y.H. Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl. Math. Comput. 2016, 285, 1–7.
- 7.
Cai, Z.; Huang, L.; Guo, Z.; et al. On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions. Neural Netw. 2012, 33, 97–113.
- 8.
Forti, M.; Nistri, P.; Papini, D. Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. I Regul. Pap. 2003, 50, 1421–1435.
- 9.
Kong, F.C.; Fang, X.W. Dynamic behavior of a class of neutral-type neural networks with discontinuous activations and time-varying delays. Appl. Intell. 2018, 48, 4834–4854.
- 10.
Kong, F.C. Dynamical behaviors of the generalized hematopoiesis model with discontinuous harvesting terms. Int. J. Biomath. 2019, 12, 1950009.
- 11.
Kong, F.C.; Zhu, Q.X.; Liang, F.; et al. Robust fixed-time synchronization of discontinuous Cohen-Grossberg neural networks with mixed time delays. Nonlinear Anal. Model. Control 2019, 24, 603–625.
- 12.
Kong, F.C.; Nieto, J.J. Almost periodic dynamical behaviors of the hematopoiesis model with mixed discontinuous harvesting terms. Discrete Contin. Dyn. Syst. B 2019, 24, 5803–5830.
- 13.
Kong, F.C.; Zhu, Q.X.;Wang, K.; et al. Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and D operator. J. Frankl. Inst. 2019, 356, 11605–11637.
- 14.
Kong, F.C.; Zhu, Q.X.; Sakthivel, R. Finite-time and fixed-time synchronization control of fuzzy Cohen-Grossberg neural networks. Fuzzy Sets Syst. 2020, 394, 87–109.
- 15.
Lu, W.; Chen, T. Dynamical behaviors of delayed neural networks systems with discontinuous activation functions. Neural Comput. 2006, 18, 683–708.
- 16.
Liu, X.; Cao, J. Robust state estimation for neural networks with discontinuous activations. IEEE Trans. Syst. Man Cybern. B Cybern. 2010, 40, 1425–1437.
- 17.
Liang, J.; Gong, W.; Huang, T. Multistability of complex-valued neural networks with discontinuous activation functions. Neural Netw. 2016, 84, 125–142.
- 18.
Wang, Z.; Cao, J.; Guo, Z.; et al. Generalized stability for discontinuous complex-valued Hopfield neural networks via differential inclusions. Proc. R. Soc. A 2018, 474, 20180507.
- 19.
Cai, Z.; Huang, L. Generalized Lyapunov approach for functional differential inclusions. Automatica 2020, 113, 108740.
- 20.
Filippov, A.F. Differential Equations with Discontinuous Right-Hand Sides; Kluwer Academic Publishers: Boston, MA, USA, 1988.
- 21.
Corduneanu, C. Almost Periodic Functions, 2nd ed.; AMS Chelsea Publishing: New York, NY, USA, 1989.
- 22.
Levitan, B.M.; Zhikov, V.V. Almost Periodic Functions and Differential Equations; Cambridge University Press: Cambridge, UK, 1982.
- 23.
Alzabut, J.O.; Nieto, J.J.; Stamov, G.T. Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis. Bound. Value Probl. 2009, 2009, 1–10.
- 24.
Alzabut, J.O. Almost periodic solutions for an impulsive delay Nicholson’s blowflies model. J. Comput. Appl. Math. 2010, 234, 233–239.
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