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https://www.selleckchem.com/products/pci-32765.html We study the collective dynamics of a heterogeneous population of globally coupled active rotators subject to intrinsic noise. The theory is constructed on the basis of the circular cumulant approach, which yields a low-dimensional model reduction for the macroscopic collective dynamics in the thermodynamic limit of an infinitely large population. With numerical simulation, we confirm a decent accuracy of the model reduction for a moderate noise strength; in particular, it correctly predicts the location of the bistability domains in the parameter space.We study scenarios of the appearance of strange homoclinic attractors (which contain only one fixed point of saddle type) for one-parameter families of three-dimensional non-orientable maps. We describe several types of such scenarios that lead to the appearance of discrete homoclinic attractors including Lorenz-like and figure-8 attractors (which contain a saddle fixed point) as well as two types of attractors of spiral chaos (which contain saddle-focus fixed points with the one-dimensional and two-dimensional unstable manifolds, respectively). We also emphasize peculiarities of the scenarios and compare them with the known scenarios in the orientable case. Examples of the implementation of the non-orientable scenarios are given in the case of three-dimensional non-orientable generalized Hénon maps.In this article, we investigate the dynamics of non-Bayesian social learning model with periodically switching structures. Unlike the strongly connectedness conditions set for the temporal connecting networks of the non-Bayesian social learning to guarantee its convergence in the literature, our model configurations are essentially relaxed in a manner that the connecting networks in every switching duration can be non-strongly connected. Mathematically and rigorously, we validate that, under relaxed configurations, dynamics of our model still converge to a true state of

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