查看更多>>摘要：This paper studies impulsive second-order stochastic differential systems in a separable Hilbert space X. By using the projection operators, we restrict the given problem to a finite-dimensional subspace. The existence and convergence of estimated solutions for the considered problem are investigated via the theories of cosine family and fractional powers of a closed linear operator. We also examine the existence and convergence of the Faedo-Galerkin approximate solutions. At last, we are constructed some examples to demonstrate the effectiveness of the obtained results. (c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：Community detection is a fundamental and important problem in network science, as community structures often reveal both topological and functional relationships between different components of the complex system. In this paper, we first propose a gradient descent framework of modularity optimization called vector-label propagation algorithm (VLPA), where a node is associated with a vector of continuous community labels instead of one label. Retaining weak structural information in vector-label, VLPA outperforms some well-known community detection methods, and particularly improves the performance in networks with weak community structures. Further, we incorporate stochastic gradient strategies into VLPA to avoid stuck in the local optima, leading to the stochastic vector-label propagation algorithm (sVLPA). We show that sVLPA performs better than Louvain Method, a widely used community detection algorithm, on both artificial benchmarks and realworld networks. Our theoretical scheme based on vector-label propagation can be directly applied to highdimensional networkswhere each node hasmultiple features, and can also be used for optimizing other partition measures such as modularity with resolution parameters. (C) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：The (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani (KdVSKR) equation which consists of the KdV equation and the SK equation is studied. Soliton molecules of the KdVSKR equation are given by means of the velocity resonance mechanism. By selecting the values of the phases, soliton molecule bounded by the three solitons is transferred to other type of the soliton molecule bounded by the asymmetric soliton and one soliton. Multi-breather solutions are derived by selecting the complex conjugate relations in the parameters. The relative positions for the maximum amplitudes of the multi-breathers can adjust with different values of the phases. It demonstrates that the phases of the multi-soliton solutions play an important effect in certain phenomena. In the meanwhile, the interactions between a soliton molecule and one-order breather, and between a soliton molecule and one-order lump of the KdVSKR equation are analyzed. The interactions are an elastic collisions by both the analytical and graphical ways.
Klinshov, Vladimir V.Kovalchuk, Andrey V.Franovic, IgorPerc, Matjaz...
7页
查看更多>>摘要：Rate chaos is a collective state of a neural network characterized by slow irregular fluctuations of firing rates of individual neurons. We study a sparsely connected network of spiking neurons which demonstrates three different scenarios for the emergence of rate chaos, based either on increasing the synaptic strength, increasing the synaptic integration time, or clustering of the excitatory synaptic connections. Although all the scenarios lead to collective dynamics with similar statistical features, it turns out that the implications for the computational capability of the network in performing a simple delay task are strongly dependent on the particular scenario. Namely, only the scenario involving slow dynamics of synapses results in an appreciable extension of the network's dynamic memory. In other cases, the dynamic memory remains short despite the emergence of long timescales in the neuronal spike trains. (c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
Soukaina, Ben RhilaImane, AgmourMostafa, RachikNaceur, Achtaich...
8页
查看更多>>摘要：Recently, some planktonic organisms have been put to use in biotechnological applications, and their usefulness has been discovered in the development of alternative and healthy foods, natural medicines, and cosmetics. Therefore, the management of plankton production is a major challenge for the development of aquaculture. In order to achieve this goal, chlorophyll a, a pigment present in all photosynthetic organisms, is generally and historically used as an estimator of the biomass of planktonic organisms. In this work, we propose a bioeconomic spatiotemporal discrete model ina multi-fishing zone to describe the predation interaction between phytoplank-ton and zooplankton (Crustacean) organisms by taking into consideration the harvesting activity. To guarantee the survival of two organisms, we consider two harvesting control strategies. The existence of optimal controls and their characterization are proved by using the discrete version of Pontryagin's maximum principle. Based on the concentration of chlorophyll a in the maritime zones of Morocco, we control and compare the biomass of the planktonic organisms in two situations (without and with control). As a major result, we found that after controlling the exploitation of planktonic organisms, their biomasses achieve a level that can ensure their sustainability. The achieved outcomes in the numerical simulations are given by using the forward-backward sweep method (FBSM). (c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：In the present paper we investigate two cases which can explain what happens when the Cournot equilibrium of a duopoly model loses stability through a Neimark-Sacker bifurcation of subcritical type. This kind of bifurcation involves complex dynamics which lead to the appearance of closed invariant curves. We analyze a Cournot model where competitors hold different plants and compete on advertising quantities. The model is described by a two-dimensional piecewise map in discrete time. Making use of analytical results and numerical simulations, we show that the appearance/disapearance of closed invariant curves is directly related to two different mecha-nisms, namely homoclinic bifurcations and border collision bifurcations.(c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：In the financial market, the stock association network can be used to describe the correlations between stock prices. The rise and fall of stock prices and their mutual influence can be described by a reversible cascading failure process. In the reversible spreading processes, the influence of fluctuation of an individ-ual stock price on companies, industries and even the financial markets can be regarded as the influence of the individual stock in the financial networks. In this paper, based on the stock price association net-works of nine sectors in China A-stock market, we studied the identification of the most influential nodes in the reversible spreading processes. It is found that due to the high proportion of core nodes in the stock association networks, the k-coreness centrality can not accurately measure the influence of these nodes. A large number of simulations show that the number of out-leaving edges of neighbor nodes can better evaluate the influence of a node in the spreading processes. Then a node strength centrality and s- coreness centrality based on link importance are developed to measure the spreading influence of nodes. Compared with degree centrality and k-coreness centrality, the node strength and s-coreness based on strength have a better performance in identifying the most influential nodes. The ranking algorithm con-sidering the structures and dynamics of local neighbors can further improve the ranking performance. The proposed framework and ranking method open up a new idea in identifying the most influential stocks in financial networks. (c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：The inability of Albert Einstein and quantum physicists to resolve whether the laws of nature operate exactly or probabilistically impacted scientific methodology. Karl Popper further compounded the problem by stressing empirical falsifiability and proposing causes cannot be proven because of infinite regress. For these and other reasons, many investigators either downplayed propositions of cause or even ridiculed them. With causality vilified, metaphysics took a back seat to empirical science. In Earth sciences, however, causality remains a top priority. Thus, a significant interdisciplinary rift developed in established scientific procedures. Yet, some physicists still wanted to know why their equations worked, and some still postulated causality despite its diminished stature. Metaphysics has a rightful place in science and revive a forgotten approach, consupponibility, for testing metaphysical assumptions and theories. A set of fundamental assumptions and theories are consupponible if they exist without contradicting one another. Importantly, a single contradiction among the set falsifies the entire paradigm. To demonstrate the concepts associated with fundamental assumptions and a paradigm, this work analyses a paradigm based on infinitely fractal matter. Just like Popperian falsifiability, a large set of prohibitive fundamental assumptions allows proponents, opponents, and undecided investigators a means for falsifying the infinitely fractal universe model if the paradigm incorrectly describes the universe. That is, the goal is never to prove the paradigm, which is impossible. Instead, the goal is to attempt to disprove the paradigm by finding contradictions. Repeated failures to disprove the paradigm increase the likelihood of its correctness. (c) 2022 Elsevier Ltd. All rights reserved.
Fang, YinWu, Gang-ZhouKudryashov, Nikolay A.Wang, Yue-Yue...
13页
查看更多>>摘要：In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law constrained neural network methodwith the flexible learning rate to predict solutions and parameters of nonlinear wave models. As some examples, we study real and complex typical nonlinear wave models, including nonlinear Schrodinger equation, Korteweg-de Vries and modified Korteweg-de Vries equations. Comparedwith the traditional physics-informed neural network method, this newmethod can more accurately predict solutions and parameters of some specific nonlinear wave models even when less information is needed, for example, in the absence of the boundary conditions. This provides a reference to further study solutions of nonlinear wave models by combining the deep learning and the integrable theory.
查看更多>>摘要：The crosstalk between synapses has a far-reaching impact on the specificity of synaptic communication in human brain. Therefore, the influence of synaptic crosstalk on the dynamic behaviors of neural network cannot be ignored. In this paper, we investigate the dynamics of fractional-order (FO) memristor-coupled Hindmarsh-Rose (HR) neuron model considering synaptic crosstalk. Firstly, the equilibrium points and stability are investigated via qualitative analysis, from which it can be obtained that the number and stability of equilibrium points have diversity for different crosstalk strength parameters. Secondly, the global coexistence of multiple firing patterns is reflected by phase diagrams, Lyapunov exponent spectrums and bifurcation diagrams. The local attraction basins reveal the multi-stability phenomenon related to the initial value. The parameter related firing behaviors are described by the two-parameter bifurcation diagram. In particular, the model shows the offset boosting control method for a single variable. Then, spectral entropy (SE) and C0 complexity chaos diagram are used to observe the change of system complexity when two parameters change simultaneously. Finally, the digital implementations based on ARM are given to verify the consistency with the numerical simulation results. (C)& nbsp;2022 Published by Elsevier Ltd.
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