Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network
Studying the firing dynamics and phase synchronization behavior of heterogeneous coupled networks helps us understand the mechanism of human brain activity. In this study, we propose a novel small heterogeneous coupled network in which the 2D Hopfield neural network (HNN) and the 2D Hindmarsh–Rose (...
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| Format: | Article |
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/11/818 |
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| author | Mengjiao Wang Jiwei Peng Shaobo He Xinan Zhang Herbert Ho-Ching Iu |
| author_facet | Mengjiao Wang Jiwei Peng Shaobo He Xinan Zhang Herbert Ho-Ching Iu |
| author_sort | Mengjiao Wang |
| collection | DOAJ |
| description | Studying the firing dynamics and phase synchronization behavior of heterogeneous coupled networks helps us understand the mechanism of human brain activity. In this study, we propose a novel small heterogeneous coupled network in which the 2D Hopfield neural network (HNN) and the 2D Hindmarsh–Rose (HR) neuron are coupled through a locally active memristor. The simulation results show that the network exhibits complex dynamic behavior and is different from the usual phase synchronization. More specifically, the membrane potential of the 2D HR neuron exhibits five stable firing modes as the coupling parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula> changes. In addition, it is found that in the local region of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula>, the number of spikes in bursting firing increases with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula>. More interestingly, the network gradually changes from synchronous to asynchronous during the increase in the coupling parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula> but suddenly becomes synchronous around the coupling parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula> = 1.96. As far as we know, this abnormal synchronization behavior is different from the existing findings. This research is inspired by the fact that the episodic synchronous abnormal firing of excitatory neurons in the hippocampus of the brain can lead to diseases such as epilepsy. This helps us further understand the mechanism of brain activity and build bionic systems. Finally, we design the simulation circuit of the network and implement it on an STM32 microcontroller. |
| first_indexed | 2024-03-09T16:49:12Z |
| format | Article |
| id | doaj.art-b233f8f89b0b490cb3713e9038795a82 |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-09T16:49:12Z |
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| series | Fractal and Fractional |
| spelling | doaj.art-b233f8f89b0b490cb3713e9038795a822023-11-24T14:43:05ZengMDPI AGFractal and Fractional2504-31102023-11-0171181810.3390/fractalfract7110818Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled NetworkMengjiao Wang0Jiwei Peng1Shaobo He2Xinan Zhang3Herbert Ho-Ching Iu4School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, ChinaSchool of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, ChinaSchool of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, ChinaSchool of Electrical, Electronic and Computer Engineering, University of Western Australia, Crawley, WA 6009, AustraliaSchool of Electrical, Electronic and Computer Engineering, University of Western Australia, Crawley, WA 6009, AustraliaStudying the firing dynamics and phase synchronization behavior of heterogeneous coupled networks helps us understand the mechanism of human brain activity. In this study, we propose a novel small heterogeneous coupled network in which the 2D Hopfield neural network (HNN) and the 2D Hindmarsh–Rose (HR) neuron are coupled through a locally active memristor. The simulation results show that the network exhibits complex dynamic behavior and is different from the usual phase synchronization. More specifically, the membrane potential of the 2D HR neuron exhibits five stable firing modes as the coupling parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula> changes. In addition, it is found that in the local region of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula>, the number of spikes in bursting firing increases with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula>. More interestingly, the network gradually changes from synchronous to asynchronous during the increase in the coupling parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula> but suddenly becomes synchronous around the coupling parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math></inline-formula> = 1.96. As far as we know, this abnormal synchronization behavior is different from the existing findings. This research is inspired by the fact that the episodic synchronous abnormal firing of excitatory neurons in the hippocampus of the brain can lead to diseases such as epilepsy. This helps us further understand the mechanism of brain activity and build bionic systems. Finally, we design the simulation circuit of the network and implement it on an STM32 microcontroller.https://www.mdpi.com/2504-3110/7/11/818Hindmarsh–Rose neuronHopfield neural networkheterogeneous coupledfiring patternsphase synchronization |
| spellingShingle | Mengjiao Wang Jiwei Peng Shaobo He Xinan Zhang Herbert Ho-Ching Iu Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network Fractal and Fractional Hindmarsh–Rose neuron Hopfield neural network heterogeneous coupled firing patterns phase synchronization |
| title | Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network |
| title_full | Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network |
| title_fullStr | Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network |
| title_full_unstemmed | Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network |
| title_short | Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network |
| title_sort | phase synchronization and dynamic behavior of a novel small heterogeneous coupled network |
| topic | Hindmarsh–Rose neuron Hopfield neural network heterogeneous coupled firing patterns phase synchronization |
| url | https://www.mdpi.com/2504-3110/7/11/818 |
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