Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and ApplicationsRead the full article
Complexity publishes original research and review articles across a broad range of disciplines with the purpose of reporting important advances in the scientific study of complex systems.
Chief Editor, Prof Sayama, is currently researching complex dynamical networks, human and social dynamics, artificial life, and interactive systems while working at Binghamton University, State University of New York.
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Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays
The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays.
A New Multivariable Grey Convolution Model Based on Simpson’s Rule and Its Applications
Accurate estimations can provide a solid basis for decision-making and policy-making that have experienced some kind of complication and uncertainty. Accordingly, a multivariable grey convolution model (GMC (1, n)) having correct solutions is put forward to deal with such complicated and uncertain issues, instead of the incorrect multivariable grey model (GM (1, n)). However, the conventional approach to computing background values of the GMC (1, n) model is inaccurate, and this model’s forecasting accuracy cannot be expected. Thereby, the drawback analysis of the GMC (1, n) model is conducted with mathematical reasoning, which can explain why this model is inaccurate in some applications. In order to eliminate the drawbacks, a new optimized GMC (1, n), shorted for OGMC (1, n), is proposed, whose background values are calculated based on Simpson’ rule that is able to efficiently approximate the integration of a function. Furthermore, its extended version that uses the Gaussian rule to discretize the convolution integral, abbreviated as OGMCG (1, n), is proposed to further enhance the model’s forecasting ability. In general, these two optimized models have such advantages as simplified structure, consistent forecasting performance, and satisfactory efficiency. Three empirical studies are carried out for verifying the above advantages of the optimized model, compared with the conventional GMC (1, n), GMCG (1, n), GM (1, n), and DGM (1, n) models. Results show that the new background values can effectively be calculated based on Simpson’s rule, and the optimized models significantly outperform other competing models in most cases.
Approximation of Interactive Betweenness Centrality in Large Complex Networks
The analysis of real-world systems through the lens of complex networks often requires a node importance function. While many such views on importance exist, a frequently used global node importance measure is betweenness centrality, quantifying the number of times a node occurs on all shortest paths in a network. This centrality of nodes often significantly depends on the presence of nodes in the network; once a node is missing, e.g., due to a failure, other nodes’ centrality values can change dramatically. This observation is, for instance, important when dismantling a network: instead of removing the nodes in decreasing order of their static betweenness, recomputing the betweenness after a removal creates tremendously stronger attacks, as has been shown in recent research. This process is referred to as interactive betweenness centrality. Nevertheless, very few studies compute the interactive betweenness centrality, given its high computational costs, a worst-case runtime complexity of O(N4) in the number of nodes in the network. In this study, we address the research questions, whether approximations of interactive betweenness centrality can be obtained with reduction of computational costs and how much quality/accuracy needs to be traded in order to obtain a significant reduction. At the heart of our interactive betweenness approximation framework, we use a set of established betweenness approximation techniques, which come with a wide range of parameter settings. Given that we are interested in the top-ranked node(s) for interactive dismantling, we tune these methods accordingly. Moreover, we explore the idea of batch removal, where groups of top-k ranked nodes are removed before recomputation of betweenness centrality values. Our experiments on real-world and random networks show that specific variants of the approximate interactive betweenness framework allow for a speedup of two orders of magnitude, compared to the exact computation, while obtaining near-optimal results. This work contributes to the analysis of complex network phenomena, with a particular focus on obtaining scalable techniques.
Equilibrium Further Studied for Combined System of Cournot and Bertrand: A Differential Approach
In general, quantity competition and price competition exist simultaneously in a dynamic economy system. Whether it is quantity competition or price competition, when there are more than three companies in one market, the equilibrium points will become chaotic and are very difficult to be derived. This paper considers generally dynamic equilibrium points of combination of the Bertrand model and Cournot model. We analyze general equilibrium points of the Bertrand model and Cournot model, respectively. A general equilibrium point of the combination of the Cournot model and Bertrand model is further investigated in two cases. The theory of spatial agglomeration and intermediate value theorem are introduced. In addition, the stability of equilibrium points is further illustrated on celestial bodies motion. The results show that at least a general equilibrium point exists in combination of Cournot and Bertrand. Numerical simulations are given to support the research results.
Risk Assessments of Water Inrush from Coal Seam Floor during Deep Mining Using a Data Fusion Approach Based on Grey System Theory
With the increase in depth of coal mining, the hydrogeological complexity largely increases and water inrush accidents happen more frequently. For the safety of coal mining, horizontal directional drilling and grouting techniques have been implemented to detect and plug the fractures and conduits that deliver high-pressure groundwater to coal mine. Taking the grouting engineering performed at Xingdong coal mine at 980 m below sea level as an example, we collected the data of grouting quantity, the loss of drilling fluid, gamma value, water temperature, average water absorption, distance between grouting loss points, water pressure on coal seam floor, and aquifuge thickness at 90 boreholes in the mine to conduct grey relational analysis, first. The analysis showed that the grouting quantity was highly correlated with all other factors. Subsequently, grey system evaluation was used to evaluate the risk of water inrush from the coal seam floor. The results of risk analysis illustrated that three water inrushes from Ordovician limestone occurred in mining face 2127, 2125, and 2222 in the study area were all located in the area with a risk score higher than 65. Through grouting, the identified cracks were effectively blocked and waterproof layers beneath the coal seam floors were constructed to reduce the threat of water inrush. By comparing the risk assessment results with three water inrush cases before grouting operation, we found that water inrush areas were consistent with the area of higher risk.
Navigating Deeply Uncertain Tradeoffs in Harvested Predator-Prey Systems
Multiple fisheries have collapsed as a result of overfishing and strong limitations in our knowledge of system conditions and consequential ecological interactions. Fishery managers need to establish harvesting strategies that balance economic benefits against ecological objectives, including avoiding unintended catastrophic consequences. Our results show that classical assumptions for fisheries management can yield severe instabilities in our quantified views of socioecological tradeoffs, making their ability to inform stakeholder preferences questionable. The complex ecological interactions implied by different parameterizations of such systems yield highly complex and nonlinear dynamic properties with multiple distinct basins of attraction. We show that small changes in our deeply uncertain representations of predator-prey systems can fundamentally shift their dynamics and the validity of candidate management strategies for harvest. Insights from this study highlight the importance of ensuring models capture deep uncertainties, as well as a breadth of financial and ecological criteria when searching for robust management options for resilient fisheries.