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361.
We introduce simplicial persistence, a measure of time evolution of motifs in networks obtained from correlation filtering. We observe long memory in the evolution of structures, with a two power law decay regimes in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both a topological embedding network filtering technique called TMFG and by thresholding, showing that the TMFG method identifies high order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their efficiency and liquidity. We find that more liquid markets tend to have a slower persistence decay. This appears to be in contrast with the common understanding that efficient markets are more random. We argue that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks. 相似文献
362.
Dynamic Analysis of an Impulsive Chemostat Model with Microbial Competition and Nonlinear Perturbation 下载免费PDF全文
In this paper, we propose an impulsive chemostat model with microbial competition and nonlinear perturbation. First, thresholds for the extinction of both microoganisms are given. Second, we investigate the persistence in mean and boundedness of the chemostat system by constructing Lyapunov function. Moreover, we obtain the sufficient condition for the existence of an ergodic stationary distribution of the system. At last, numerical simulations are presented, and the results show that the competition between two species tends to make one species disappear from their common habitat, especially when the competition is concentrated in a single resource. 相似文献
363.
Dynamical Behavior of a Stochastic Nutrient-Plankton Food Chain Model with L\''{e}vy Jumps 下载免费PDF全文
In aquatic ecosystem, plankton populations are easily affected by environmental fluctuations due to the unpredictability of many physical factors. To better understand how environmental fluctuations influence plankton populations, in this paper, we propose and investigate a stochastic nutrient-plankton food chain model with L$\acute{\rm e}$vy jumps. Firstly, by constructing a suitable Lyapunov function, we prove that the stochastic model has a unique global positive solution for any given positive initial value. Then, we establish sufficient conditions for the persistence and extinction of plankton. Finally, we provide some numerical simulations to illustrate the analytical results. 相似文献
364.
Dynamics Behavior of a Stochastic Predator-Prey Model with Stage Structure for Predator and L\''{e}vy Jumps 下载免费PDF全文
In order to study the effects of external environmental noise on the interaction dynamics between predator and prey populations, in this paper, we develop a predator-prey model with the stage structure for predator and L$\acute{\rm e}$vy noise. By constructing an appropriate Lyapunov function, we first prove that the proposed model exists the uniqueness of global positive solution. Then, we analyze the persistence and extinction of the proposed model. Finally, we perform some numerical simulations to verify the correctness of the theoretical results. 相似文献