Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay

Lin, Jiazhe; Xu, Rui; Li, Liangchen

doi:10.1016/j.cnsns.2020.105241

Cited by 27 publications

(8 citation statements)

References 21 publications

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“…x [40]. Therefore, the new equilibrium point of HSDC is shown in equation (20), and the new equilibrium point of HSDCST under load disturbance is given in equation ( 21), where the subscript E represents the value of each variable at equilibrium point.…”

Section: A Exact Linearizationmentioning

confidence: 99%

Synergetic Control Strategy for Water Hammer Wave and Mass Wave in Hydropower Station With Downstream Channel

et al. 2022

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This paper investigates the synergetic control strategy for water hammer wave and mass wave in hydropower station with downstream channel. Firstly, the mathematical model of hydropower station with downstream channel (HSDC) and hydropower station with downstream channel and surge tank (HSDCST) are established. Then, the controller formula of HSDC and HSDCST are derived on the basis of the synergetic theory. Furthermore, it is parsed that the dynamic characteristics of HSDC and HSDCST to various disturbances under synergetic control strategy. Finally, the robustness and applicability of synergetic control strategy for HSDC and HSDCST are analyzed. The results indicate that the macro variable is the linear combination of state variables and their derivatives based on feedback linearization of the state equation. For the hydropower station under the synergetic control strategy, it has excellent dynamic characteristics employing sensitive response, small overshoot, fast attenuation speed and no static error. The synergetic control strategy is superior to the PID control strategy under various disturbances in controlling the amplitude of water hammer wave in HSDC, which is down 12.5%. The attenuation of mass wave in HSDCST under synergetic control strategy is faster, and the settling time is 6.16s less than that of PID control strategy. The synergetic control strategy is superior to the PID control strategy under various disturbances in controlling the amplitude of water hammer wave in HSDC and the attenuation of mass wave in HSDCST. Compared with PID control strategy, it is the robustness of synergetic control strategy that are much more advantageous for HSDC and HSDCST. Specifically, RI value is about 1.65, 0.18 for HSDC and 2.21, 0.25 for HSDCST under synergetic control strategy, while it is about 3.05, 1.20 and 3.32, 1.30 under PID control strategy. Moreover, the synergetic control strategy has a wide applicability in controlling the water hammer wave in HSDC and mass wave in HSDCST.

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Section: A Exact Linearizationmentioning

confidence: 99%

Synergetic Control Strategy for Water Hammer Wave and Mass Wave in Hydropower Station With Downstream Channel

et al. 2022

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“…Liu et al found that cross-diffusion could lead to Turing instability of periodic solutions ( 13 , 14 ). Lin et al analyzed the conditions of Turing-Hopf bifurcation and the spatiotemporal dynamics near the bifurcation point in diffusion neural networks with time delay ( 15 ). Mondal et al studied the dynamical behaviors near the Turing-Hopf bifurcation points of the neural model.…”

Section: Introductionmentioning

confidence: 99%

Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

Wang

Shen

2023

Front. Psychiatry

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IntroductionThe study of brain function has been favored by scientists, but the mechanism of short-term memory formation has yet to be precise.Research problemSince the formation of short-term memories depends on neuronal activity, we try to explain the mechanism from the neuron level in this paper.Research contents and methodsDue to the modular structures of the brain, we analyze the pattern properties of the FitzHugh-Nagumo model (FHN) on a multilayer network (coupled by a random network). The conditions of short-term memory formation in the multilayer FHN model are obtained. Then the time delay is introduced to more closely match patterns of brain activity. The properties of periodic solutions are obtained by the central manifold theorem.ConclusionWhen the diffusion coeffcient, noise intensity np, and network connection probability p reach a specific range, the brain forms a relatively vague memory. It is found that network and time delay can induce complex cluster dynamics. And the synchrony increases with the increase of p. That is, short-term memory becomes clearer.

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“…In [10], Cheng and Xie introduced time delay into a class of triangular neural network models, studied the stability of the zero equilibrium using the characteristic equation, and provided the critical value for Hopf bifurcation. Lin and Xu [11] presented a class of reaction-diffusion neural network models with leakage delays and obtained sufficient conditions for the model to generate Hopf bifurcation with time delays. Mao and Wang established a class of multi-delay four-coupling neural network models and studied the dynamic behavior changes generated at the equilibrium point by introducing different types of time delays from the literature into the model [12].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behavior of a Class of Six-Neuron Fractional BAM Neural Networks

Liao

et al. 2023

Fractal Fract

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In this paper, the stability and Hopf bifurcation of a six-neuron fractional BAM neural network model with multiple delays are considered. By transforming the multiple-delays model into a fractional-order neural network model with a delay through the variable substitution, we prove the conditions for the existence of Hopf bifurcation at the equilibrium point. Finally, our results are verified by numerical simulations.

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Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay

Cited by 27 publications

References 21 publications

Synergetic Control Strategy for Water Hammer Wave and Mass Wave in Hydropower Station With Downstream Channel

Synergetic Control Strategy for Water Hammer Wave and Mass Wave in Hydropower Station With Downstream Channel

Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

Dynamic Behavior of a Class of Six-Neuron Fractional BAM Neural Networks

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