New criteria on global Mittag-Leffler synchronization for Caputo-type delayed Cohen-Grossberg Inertial Neural Networks

Hongmei Zhang; Xiangnian Yin; Hai Zhang; Weiwei Zhang; Hongmei Zhang; Xiangnian Yin; Hai Zhang; Weiwei Zhang

doi:10.3934/math.20231497

AIMS Mathematics

2023, Volume 8, Issue 12: 29239-29259. doi: 10.3934/math.20231497

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New criteria on global Mittag-Leffler synchronization for Caputo-type delayed Cohen-Grossberg Inertial Neural Networks

1.
School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
2.
Key Laboratory of Modeling, Simulation and Control of Complex Ecosystem in Dabie Mountains of Anhui Higher Education Institutes, Anqing Normal University, Anqing 246133, China

Received: 30 August 2023 Revised: 01 October 2023 Accepted: 15 October 2023 Published: 26 October 2023
MSC : 26A33, 92B20, 94B50

Our focus of this paper is on global Mittag-Leffler synchronization (GMLS) of the Caputo-type Inertial Cohen-Grossberg Neural Networks (ICGNNs) with discrete and distributed delays. This model takes into account the inertial term as well as the two types of delays, which greatly reduces the conservatism with respect to the model. A change of variables transforms the $ 2\beta $ order inertial frame into $ \beta $ order ordinary frame in order to deal with the effect of the inertial term. In the following steps, two novel types of delay controllers are designed for the purpose of reaching the GMLS. In conjunction with the novel controllers, utilizing differential mean-value theorem and inequality techniques, several criteria are derived to determine the GMLS of ICGNNs within the framework of Caputo-type derivative and calculus properties. At length, the feasibility of the results is further demonstrated by two simulation examples.
- Caputo derivative,
- Cohen-Grossberg Neural Networks,
- global Mittag-Leffler synchronization,
- inertial,
- delays
Citation: Hongmei Zhang, Xiangnian Yin, Hai Zhang, Weiwei Zhang. New criteria on global Mittag-Leffler synchronization for Caputo-type delayed Cohen-Grossberg Inertial Neural Networks[J]. AIMS Mathematics, 2023, 8(12): 29239-29259. doi: 10.3934/math.20231497

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Abstract

Our focus of this paper is on global Mittag-Leffler synchronization (GMLS) of the Caputo-type Inertial Cohen-Grossberg Neural Networks (ICGNNs) with discrete and distributed delays. This model takes into account the inertial term as well as the two types of delays, which greatly reduces the conservatism with respect to the model. A change of variables transforms the $ 2\beta $ order inertial frame into $ \beta $ order ordinary frame in order to deal with the effect of the inertial term. In the following steps, two novel types of delay controllers are designed for the purpose of reaching the GMLS. In conjunction with the novel controllers, utilizing differential mean-value theorem and inequality techniques, several criteria are derived to determine the GMLS of ICGNNs within the framework of Caputo-type derivative and calculus properties. At length, the feasibility of the results is further demonstrated by two simulation examples.

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