Time-varying Coupling Strength Research Articles

The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain

The Kuramoto model of the describing neuronal synchrony is mathematically investigated in the brain. A general analytical solutions (the most sententious description) for the Kuramoto model, incorporating the inclusion of a Ki,j(t) term to represent time-varying coupling strengths, have been obtained by using the precise mathematical approach. We derive an exact analytical expression, opening out the connotative and latent linear relation, for the mathematical character of the phase configurations in the Kuramoto model of the describing neuronal synchrony in the brain.

Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength

A new robust adaptive synchronization approach for the global synchronization of complex dynamical networks is proposed. Both the characteristics of the uncoupled nodes of the network and the coupling matrix are unknown, but only a time-varying coupling strength is used in this paper. Based on the LaSalle–Yoshizawa theorem and by introducing an update law, a sufficient condition of the global synchronization is obtained. The update law is only dependent on the states of the complex dynamical network, which do not need any other information such as the characteristic of the uncoupled nodes of the network and the second largest eigenvalue of the coupling matrix. Compared with the existing results, our synchronization strategy is still useful when the existing synchronization methods become invalid. Moreover, it is very convenient to use. An example of the complex network is finally used to verify the proposed theoretical result.

Generalising the Kuramoto model for the study of neuronal synchronisation in the brain

In this article, we have generalised the Kuramoto model to allow one to model neuronal synchronisation more appropriately. The generalised version allows for different connective arrangements, time-varying natural frequencies and time-varying coupling strengths to be realised within the framework of the original Kuramoto model. By incorporating the above mentioned features into the original Kuramoto model one can allow for the adaptive nature of neurons in the brain to be accommodated. Extensive tests using the generalised Kuramoto model were performed on a N = 4 coupled oscillator network. Examination of how different connective arrangements, time-varying natural frequencies and time-varying coupling strengths affected synchronisation separately and in combination are reported. The effects on synchronisation for large N are also reported.

Time-varying coupling strengths, nuclear forces and unification

We investigate the dependence of the nucleon–nucleon force in the deuteron system on the values of coupling strengths at high energy, which will in general depend on the geometry of extra dimensions. The stability of deuterium at all times after nucleosynthesis sets a bound on the time variation of the ratio of the QCD confinement scale to light quark masses. We find the relation between this ratio, which is exponentially sensitive to high-energy couplings, and fundamental parameters, in various classes of unified theory. Model-dependent effects in the Higgs and fermion mass sector may dominate even over the strong dependence of the QCD scale Λ. The binding energy of the deuteron also has an important effect on nucleosynthesis: we estimate the resulting bounds on variation of couplings.