Bifurcation dynamics of natural drainage networks

Bifurcation dynamics of natural drainage networks.

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relations...

Bifurcation analysis and dynamics of a Lorenz –type dynamical system 

./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcati...

Bifurcation Phenomena of Opinion Dynamics in Complex Networks

In this paper, we study the opinion dynamics of Improved Deffuant model (IDM), where the convergence parameter μ is a function of the opposite’s degree K according to the celebrity effect, in smallworld network (SWN) and scale-free network (SFN). Generically, the system undergoes a phase transition from the plurality state to the polarization state and to the consensus state as the confidence p...

Dynamics and Bifurcation of Neural

Natural Langevin Dynamics for Neural Networks

One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGLD is a standard stochastic gradient descent to which is added a controlled am...