Parameter-dependent synchronization transition of coupled neurons with co-existing spiking and bursting

The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain

“…The CS achieved at strong coupling strength was spiking, bursting, and spiking patterns for cases 1, 2, and 3, respectively. In another investigation of case 1, the two coupled neurons exhibited different synchronization transition processes, which were dependent on the parameter values within the coexisting parameter region [35]. The CS achieved at large coupling strength was found to be either spiking when the control parameter value was closer to that of the monostable spiking or bursting patterns when the control parameter value was closer to that of the monostable bursting.…”

“…The attraction domain of the coexisting bursting and spiking is found to play important roles in understanding the dynamics of synchronization transition. Compared with previous studies [34][35][36][37], more comprehensive results are acquired and more accurate conclusions are drawn. The rest of this paper is organized as follows.…”

“…A few recent works have focused on synchronization of coupled systems composed of single units that exhibit multi-stable or coexisting behaviors when isolated [29][30][31][32][33][34][35][36][37]; for example, the coupled system composed of two Rössler-like electronic circuits with coexisting chaotic attractors [29][30][31], two coupled Hénon maps with coexisting periodic behaviors [32], two optical bi-stable systems (with coexistence of fixed point and chaos, of fixed point and periodic attractor, and of two periodic attractors) transition from nonsynchronization to complete synchronization (CS) via various complex synchronous states as the coupling strength increases [33]. In addition to these unidirectionally coupled systems, there are investigations on the bidirectionally coupled systems with coexisting behaviors [34][35][36][37].…”

“…In addition to these unidirectionally coupled systems, there are investigations on the bidirectionally coupled systems with coexisting behaviors [34][35][36][37]. In a previous study [34], the synchronization transition process of two coupled neurons with coexistence of spiking and bursting, which lies between monostable spiking and monostable bursting as the control parameter is changed, was investigated.…”

“…The CS achieved at large coupling strength was found to be either spiking when the control parameter value was closer to that of the monostable spiking or bursting patterns when the control parameter value was closer to that of the monostable bursting. Despite both investigations, multiple questions remain to be answered because only one parameter value and one initial value were considered in one study [34], and only one initial value and one case were considered in the other [35]. More recently, the attraction domain of the coexisting behaviors has been adopted to attempt to understand the dynamics of synchronization transition [36,37].…”