Synchronization Transition of Bursting Oscillations in a Half-center Oscillator Based on Time-delay Regulation
JI Fengchao1, SONG Zigen1,2
1. College of Information Technology, Shanghai Ocean University, Shanghai 201306, China; 2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Abstract：To further investigate the regulatory role of coupled time-delay on the modes of discharge activity in a half-center oscillator (HCO), based on the Hindmash-Rose (HR) neuronal model, the DHCO (delayed HCO) model with bursting behavior is constructed. By calculating phase difference between clusters of the bursting, dynamical evolution of the DHCO nervous system is studied with time-delay regulation. The DHCO system presents in-phase and anti-phase bursting oscillations in different parameter spaces. The synchronization transition of the bursting is determined under time-delay controlling. The results show that the DHCO model, regarded as the functional unit of the CPG (Central pattern generator) system can generate and switch multiple locomotion gaits by adjusting time-delay.
季丰超, 宋自根. 基于时滞调控的簇放电半中心振荡器同步模式转迁研究[J]. 复杂系统与复杂性科学, 2025, 22(3): 49-55.
JI Fengchao, SONG Zigen. Synchronization Transition of Bursting Oscillations in a Half-center Oscillator Based on Time-delay Regulation[J]. Complex Systems and Complexity Science, 2025, 22(3): 49-55.
[1] GRILLNER S, MANIRA A E. Current principles of motor control, with special reference to vertebrate locomotion[J]. Physiological Reviews, 2020, 100(1): 271-320. [2] PINTO C M A, GOLUBITSKY M. Central pattern generators for bipedal locomotion[J]. Journal of Mathematical Biology, 2006, 53(3): 474-489. [3] YU J, TAV M, CHEN J, et al. A survey on CPG-inspired control models and system implementation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2013, 25(3): 441-456. [4] BARUZZI V, LODI M, STORACE M, et al. Generalized half-center oscillators with short-term synaptic plasticity[J]. Physical Review E, 2020, 102(3): 032406. [5] LOBATO-RIOS V, RAMALINGASETTY S T, ÖZDIL P G, et al. NeuroMechFly, a neuromechanical model of adult drosophila melanogaster[J]. Nature Methods, 2022, 19(5): 620-627. [6] BERG E M, BJÖRNFORS E R, PALLUCCHI I, et al. Principles governing locomotion in vertebrates: lessons from zebrafish[J]. Frontiers in Neural Circuits, 2018, 12: 73. [7] BORISYUK R, MERRISON-HORT R, SOFFE S R, et al. To swim or not to swim: a population-level model of Xenopus tadpole decision making and locomotor behaviour[J]. BioSystems, 2017, 161: 3-14. [8] SAKURAI A, KATZ P S. The central pattern generator underlying swimming in Dendronotus iris: a simple half-center network oscillator with a twist[J]. Journal of Neurophysiology, 2016, 116(4): 1728-1742. [9] DOLOC-MIHU A, CALABRESE R L. A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity[J]. Journal of Biological Physics, 2011, 37: 263-283. [10] KOROTKOV A G, LEVANOVA T A, ZAKS M A, et al. Dynamics in a phase model of half-center oscillator: two neurons with excitatory coupling[J]. Communications in Nonlinear Science and Numerical Simulation, 2022, 104: 106045. [11] REYES M B, CARELLI P V, SARTORELLI J C, et al. A modeling approach on why simple central pattern generators are built of irregular neurons[J]. PloS One, 2015, 10(3): e0120314. [12] NAGORNOV R, OSIPOV G, KOMAROV M, et al. Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound[J]. Communications in Nonlinear Science and Numerical Simulation, 2016, 36: 175-191. [13] YU Z, THOMAS P J. Dynamical consequences of sensory feedback in a half-center oscillator coupled to a simple motor system[J]. Biological Cybernetics, 2021, 115(2): 135-160. [14] SONG Z, ZHEN B, HU D. Multiple bifurcations and coexistence in an inertial two-neuron system with multiple delays[J]. Cognitive Neurodynamics, 2020, 14: 359-374. [15] YAO S, DING L, SONG Z, et al. Two bifurcation routes to multiple chaotic coexistence in an inertial two-neural system with time delay[J]. Nonlinear Dynamics, 2019, 95: 1549-1563. [16] PARK S H, KIM S, PYO H B, et al. Effects of time-delayed interactions on dynamic patterns in a coupled phase oscillator system[J]. Physical Review E, 1999, 60(4): 4962. [17] SONG Z., XU J. Self-/mutual-symmetric rhythms and their coexistence in a delayed half-center oscillator of the CPG neural system[J]. Nonlinear Dynamics, 2022, 108: 2595-2609. [18] SONG Z., HUANG X., XU J. Spatiotemporal pattern of periodic rhythms in delayed van der pol oscillators for the CPG-based locomotion of snake-like robot[J]. Nonlinear Dynamics, 2022, 110: 3377-3393. [19] SONG Z, ZHU J, XU J. Gaits generation of quadruped locomotion for the CPG controller by the delay-coupled VDP oscillators[J]. Nonlinear Dynamics, 2023: 1-19. [20] 曹淑红, 段利霞, 唐旭晖, 等. 具有时滞的耦合Hindmarsh-Rose神经元系统的放电模式[J]. 动力学与控制学报, 2012, 10(1): 1672-6553. CAO S H, DUAN L X, TANG X H, et al. The discharge pattern of coupled hindmarsh-rose neuron system with time delay[J]. Journal of Dynamics and Control, 2012, 10(1): 1672-6553. [21] YAO C. Synchronization and multistability in the coupled neurons with propagation and processing delays[J]. Nonlinear Dynamics, 2020, 101: 2401-2411. [22] COLLENS J, PUSULURI K, KELLEY A, et al. Dynamics and bifurcations in multistable 3-cell neural networks[J]. Chaos, 2020, 30(7): 072101. [23] YI M, YAO C. A chimera oscillatory state in a globally delay-coupled oscillator network[J]. Complexity, 2020, 2020: 1-11. [24] CHEN J X, XIAO J, QIAO L Y, et al. Dynamics of scroll waves with time-delay propagation in excitable media[J]. Communications in Nonlinear Science and Numerical Simulation, 2018, 59: 331-337. [25] 张洁, 李新颖, 杨宗凯, 等. 时滞对磁通耦合及化学耦合神经元分岔及同步的影响[J]. 应用数学和力学, 2022, 43(12): 1000-0887. ZHANG J, LI X Y, YANG Z K, et al. Effects of time delay on bifurcation and synchronization of flux-coupled and chemically coupled neurons[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1000-0887.
