The Dynamics In The Complex Networks And The Computational Model Of Visual Perceptual Learning

A complex system can often be simplified to a coupled oscillator system model.The complex network can describe the coupling relationship between the oscillators.We use such a model to study the dynamic behavior of the complex system.In this thesis,we mainly discuss the coupled FitzHugh-Nagumo(FHN)model and the Kuramoto model.In addition to theoretical models,we also pay attention to the problem of visual perceptual learning in the field of neuroscience.From the perspective of dynamics,the nervous system is a high-dimensional nonlinear coupled dynamic system.There are many dynamic behaviors such as instability and synchronization in this system.These behaviors are closely related to the neural mechanisms behind visual perceptual learning.In this thesis,we first study the dynamics of the two theoretical models,and then model and calculate the nervous system involved in the visual perceptual learning problem.We hope that the study of the dynamics of the coupled oscillator system can provide insights for the study of visual perception learning problems.First,through numerical simulation and theoretical analysis,we studied the FHN oscillator system with nonlinear coupling on the duplex network.We find that the emergent patterns may be characterized by dominant network modes when the homogeneous equilibrium becomes unstable.These dominant network modes on duplex networks are related to the most unstable network modes in monolayer networks.Using these dominant networks modes,we develop two approximation methods to deal with the instability of the homogeneous equilibrium on duplex networks.By comparing with the numerical calculation results,our approximation methods are effectiveSecond,researchers generally use the Kuramoto model to study the synchronization problems.In previous work,the coupling strength between the phase oscillators is identical.However,we studied the synchronization problem in the Kuramoto model with heterogeneous coupling strength which is associated with the natural frequency of the phase oscillators.We found that by controlling the parameters of the correlation function between the coupling strength and the natural frequency,the type of synchronous phase transition can be changed between continuous and discontinuous phase transitions.Moreover,by controlling the parameters of the correlation function,we can also achieve rich synchronization states,and the types of phase transitions between these synchronization states can also be changed by controlling the correlation parameters.Finally,we carried out large-scale modeling work on the visual nerve pathways involved in visual perceptual learning.The modeled areas include the lateral geniculate body(LGN),the primary visual cortex(V1)and the secondary visual cortex(V2).Compared with previous work,our model is characterized by multiple cortical regions,and emphasizing the interaction between them.Due to the complexity of neuron connections,there are more than a dozen model parameters that we need to adjust in numerical calculations.In order to obtain a numerical solution that conforms to the experiment,we need to explore a huge parameter space.However,the analysis method of nonlinear dynamics can provide a shortcut for us to explore the parameter space.At present,we got preliminary results that can be qualitatively consistent with the experimental data of visual perceptual learning.But if we want to fully understand the dynamic mechanism behind the nervous system,it is still a very challenging task,and we need to make more efforts to this end.