Global dynamics for a class of new bistable nonlinear oscillators with bilateral elastic collisions

Author(s):  
Shuangbao Li ◽  
Tingting Wang ◽  
Xiaoli Bian

For periodically forced nonlinear oscillators permitting escape from a potential well a relation is observed between two well-known phenomena, the period-doubling cascade leading to the chaotic escape of the resonant attractor and the complex dynamics associated with the creation of a structurally unstable homoclinic orbit. The particular homoclinic orbit is identified as that created at the initial change of the period one Birkhoff signature of the invariant manifolds of the hilltop saddle. The primary resonant attractor may thus be viewed as the period one simple Newhouse orbit. Significant subharmonic and superharmonic escape events may likewise be associated with nearby Birkhoff signature changes. Significant information about the global dynamics may thus be obtained with little numerical effort by inspection of the signatures of the invariant manifolds of the hilltop saddle.


Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).


2020 ◽  
Vol 20 (6) ◽  
pp. 410-416 ◽  
Author(s):  
Ning-Ning Liu ◽  
Jing-Cong Tan ◽  
Jingquan Li ◽  
Shenghui Li ◽  
Yong Cai ◽  
...  

The outbreak of COVID-19 due to SARS-CoV-2 originally emerged in Wuhan in December 2019. As of March 22, 2020, the disease spread to 186 countries, with at least 305,275 confirmed cases. Although there has been a decline in the spread of the disease in China, the prevalence of COVID-19 around the world remains serious despite containment efforts undertaken by national authorities and the international community. In this article, we systematically review the brief history of COVID-19 and its epidemic and clinical characteristics, highlighting the strategies used to control and prevent the disease in China, which may help other countries respond to the outbreak. This pandemic emphasizes the need to be constantly alert to shifts in both the global dynamics and the contexts of individual countries, making sure that all are aware of which approaches are successful for the prevention, containment and treatment of new diseases, and being flexible enough to adapt the responses accordingly.


Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.


Author(s):  
Saskia Sassen

Although the global is often portrayed in opposition to the national, this chapter explores how the global can be structured inside the national in at least three ways that are significant for the field of global studies. They are a) the endogenizing or the localizing of global dynamics in the national milieu; b) the creation of formations that, although global, are articulated with particular actors, cultures, or projects; and c) the denationalizing of what had historically been constructed as national. Global studies research into such subnationally based processes and dynamics of globalization requires methodologies and theorizations that engage not only global scalings but also subnational scalings as components of global processes. It makes possible the use of long-standing research techniques in the study of globalization, and it provides a bridge between globalization and the wealth of national and subnational data sets.


2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Diego F. Leal ◽  
Nicolas L. Harder

AbstractEvidence from 184 countries over the span of 25 years is gathered and analyzed to understand North–North, South–South, and North–South international migration flows. Conceptually, the analysis borrows from network theory and Migration Systems Theory (MST) to develop a model to characterize the structure and evolution of international migration flows. Methodologically, the Stochastic Actor-oriented Model of network dynamics is used to jointly model the three types of flows under analysis. Results show that endogenous network effects at the monadic, dyadic, and triadic levels of analysis are relevant to understand the emergence and evolution of migration flows. The findings also show that a core set of non-network covariates, suggested by MST as key drivers of migration flows, does not always explain migration dynamics in the systems under analysis in a consistent fashion; thus, suggesting the existence of important levels of heterogeneity inherent to these three types of flows. Finally, evidence related to the role of political instability and countries’ care deficits is also discussed as part of the analysis. Overall, the results highlight the importance of analyzing flows across the globe beyond typically studied migratory corridors (e.g., North–South flows) or regions (e.g., Europe).


2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.


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