Effects Of Gradient Coupling On The Explosive Synchronization In Regular Network

The explosive synchronization of coupled oscillator systems,as one of the intrinsic mechanisms of self-organized kinetic behavior of many biological systems,has attracted much attention.At present,the well-known synchronous phase transitions are mostly continuous and non-hysteretic second-order phase transitions from chaos to synchronization in complex networks.In contrast,explosive synchronization can rapidly and discontinuously jump between two steady states in a system.This is highly similar to many phenomena in real life,Such as: neurological epilepsy,power grid cascade failure.In general,people think that explosive synchronization only exists in complex network structures.Chen Wei et al.recently found that in a regular network of symmetric coupling,the phenomenon of explosive synchronization can be observed under the special frequency distribution.Considering that the interaction between many vibrators in real life is asymmetric,a kindof gradient coupling regime is introduced into the formal symmetrical coupled oscillators.we study in detail the effect of the gradient coupling on the explosive synchronization of coupled oscillator systems in a regular network by the theoretical analysis and numerical methods.It is found that when the effective coupling strength between the nodes is positive,the gradient flow coupling significantly promotes the explosive synchronization of the coupled phase oscillator system,and the critical coupling strength required for the coupling system to achieve explosive synchronization is linearly related to the gradient coupling strength.When the effective coupling strength is negative,the gradient coupling reduces the the area of thehysteresis and the order parameter.Based on thethoretical analysis,we predict the influence mechanism and parameter range of the gradient coupling on the explosive synchronization of the coupling system.The results show that,the coupling oscillator can be divided into three areas with the specific spatial frequency arrangement,synchronous area,buffer area and nonsynchronous area.Increasing the gradient coupling will expands the synchronization area and compresses the the nonsynchronous area.Once the nonsynchronous area disappears,the oscillators in the buffer area suddenly join the synchronous area and form explosive synchronization.Moreover,even when the coupled oscillatorsare in the synchronous region,they are in bistable states.That is,under the same effective coupling strength,the phase of the nodes in the synchronization area exhibit two kinds of synchronization modesbased on the initial conditions,centralized phase locking and decentralized phaselocking.The analysis results of the two-state attraction domain show that the gradient coupling effect is beneficial to the centralized phase locking state.The research results can provide a better understanding of the main influence factors and inherent mechanisms in the transition process of coupled oscillator system from non-coherent state to synchronous state.