查看更多>>摘要：We study the Epstein zeta-function formulated on the d-dimensional hypercubic lattice zeta((d))(s) = 1/2 Sigma' (n1,...,nd) (n(1)(2) +... + n(d)(2))(-s/2) where the real part R(s) > dand the summation runs over all integers except of the origin (0, 0,..., 0). An analytical continuation of the Epstein zeta-function to the whole complex s-plane is constructed for the spatial dimension dbeing a continuous variable ranging from 0 to infinity. Zeros of the Epstein zeta-function rho = rho x + i rho(y) are defined by zeta((d)) (rho) = 0. The nontrivial zeros split into the "critical" zeros (on the critical line) with rho(x) = d/2 and the "off-critical" zeros (offthe critical line) with rho(x) not equal d/2. Numerical calculations reveal that the critical zeros form closed or semi-open curves rho(y) (d) which enclose disjunctive regions of the plane (rho(x) = d/2,rho(y)). Each curve involves a number of left/right edge points rho*= (d */2,rho*(y)), defined by a divergent tangent d(rho y)/dd|(rho'). Every edge point gives rise to two conjugate tails of off-critical zeros with continuously varying dimension dwhich exhibit a singular expansion around the edge point, in analogy with critical phenomena for second-order phase transitions. For each dimension d > 9.24555... there exists a conjugate pair of real off-critical zeros which tend to the boundaries 0 and dof the critical strip in the limit d ->infinity. As a by-product of the formalism, we derive an exact formula for lim(d -> 0)zeta((d)) (s)/d. An equidistant distribution of critical zeros along the imaginary axis is obtained for large d, with spacing between the nearest-neighbour zeros vanishing as 2 pi/ ln din the limit d ->infinity. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In multi-agent systems, the problem of a leader following consensus has been the most attractive area of research since the past decade due to its applicability in the real world problem requiring leader based control of the system such that the rest of the system achieve a common goal i.e. leaders trajectory, acted as a reference for the followers, and once this target is achieved then it is said to have a leader following consensus. In the proposed study, the same concept of leader-based consensus is suggested to develop a consensus on the identical speed of several motors connected in a network with leader following topology. In this study, each of the motorized circuits is deliberated as an i th agent, and each agent of the proposed system is considered to have the same dynamics, an essential requirement to make a multi-agent system. Moreover, the consensus control algorithm is also modified as per the requirement of the proposed problem. Furthermore, the proposed study uses an observer-based approach to deal with the aforesaid problem due to the unavailability of direct measurement of the state variable i.e. speed, in the case of multi-motor systems the required output state is motors speed, in some of the industrial applications. The stability of the proposed system is established by developing a common Lyapunov function and is simulated in MATLAB. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Scholars explored cooperative behavior on different network; however they did not consider the resource distribution and consumption on them. In our work, we propose a kind of uneven resource distribution network model, in which players can consume finite resources to survive. In our model, firstly, there are four players, and then we imitate real organism behavior, such as eating, migration, game, leaning, and reproduction. Meanwhile, during this process, finite resource also decreases with players' consumption. After numerical simulation, we find that defectors can occupy the most resource-rich areas at first, but they cannot survive in hostile area and decrease rapidly. While cooperators always keep growing. In addition, when resources decrease substantially, cooperative behavior can be promoted. This also sprouts new insights on survival and development of cooperative behavior. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we formulate a stage-structured predator-prey model with Holling-I and Crowley-Martin functional responses in deterministic and stochastic environments, where Holling-I and Crowley-Martin functional responses conform respectively to predator feeds on juvenile and adult prey. In the deterministic case, by discussing the existence and stability of equilibria as well as equilibrium point bifurcations, we observe that the model can possess more than one positive equilibrium and exhibit rich dynamics such as bistability and complex bifurcations, meaning that its dynamics is easily affected by the environmental perturbations. In the stochastic case, by constructing appropriate Lyapunov functions we establish respectively the sufficient conditions for the ergodic stationary distribution and extinction of the model. Moreover, for the bistability scenario between a positive equilibrium and an interior limit cycle in the absence of noise, we can numerically observe the phenomenon of noise-induced state frequent switching between two stochastic attractors in the bistable zone. Biologically, our results can partially explain the phenomenon that in real world, for the inevitably small environmental noise intensities, the biological populations may remain at least two patterns of survival to switch. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In social dilemmas, individual behavior generally follows the characteristics of conditional cooperation and emotional conditional cooperation. However, it is hard to adequately explain the behavior patterns of conditional cooperation with the evolutionary game theory. This paper introduces expectation-based reinforcement learning methods in the public goods game to investigate and account for the behavior patterns. Instead of letting individuals occupy the entire network as previous studies have done, we focus on studying individual behavior patterns on a network with empty nodes. The results under total population density show the effectivity of our model as they are consistent with those of the previous studies, that is, individuals' behavior exhibits conditional cooperation and its variant moody conditional cooperation. However, in the network with empty nodes, conditional cooperation shows opposite trends. We finally demonstrate that an appropriate population density can facilitate the maintenance and development of cooperation. (C) 2021 Published by Elsevier Inc.
查看更多>>摘要：This study reports adaptive neural network tracking control problem for a class of uncertain strict-feedback nonlinear systems with quantized input and the output constraint. To successfully overcome the obstacle caused by quantized input and the output constraint, the disintegration of hysteresis quantizer and a log-type Barrier Lyapunov function are exploited. During the control design, uncertain nonlinearities are approximated by radial basis function neural networks. Moreover, the number of adaptive law is only one, thereby reducing the computational burden. Under the proposed quantized tracking control scheme, the boundedness of all signals in the closed-loop system is validated and the output tracking error converges to an arbitrarily small domain of origin. At the same time, it can be ensured that the output constraint isn't violated. Finally, two simulation examples are provided to verify the effectiveness of the control scheme. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper investigates the sampled-data synchronization issue of Markovian jumping neural networks with additive time-varying delays. Firstly, a ternary quadratic function negative-determination condition and the bilateral sampled-interval-related Lyapunov functional (BSIRLF) approach are proposed. Based on the developed two novel approaches, some new criteria based on the linear matrix inequalities (LMIs) are established to guarantee the drive-response stochastic sampled-data synchronization of Markovian jumping neural networks with additive time-varying delays. Meanwhile, the corresponding sampled-data controller gains are designed under the larger sampling interval. In the end, the availability and merits of the developed approaches are displayed via two simulative examples. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：First, we apply the implicit Euler scheme to discretize the sine-Gordon lattice equation (possessing a global attractor) and prove the existence of a numerical attractor for the time-discrete sine-Gordon lattice system with small step sizes. Second, we establish the upper semi-convergence from the numerical attractor towards the global attractor when the step size tends to zero. Third, we establish the upper semi-convergence from the random attractor of the stochastic sine-Gordon lattice equation to the global attractor when the intensity of noise goes to zero. Fourth, we show the finitely dimensional approximations of the three (numerical, random and global) attractors as the dimension of the state space goes to infinity. In a word, we establish four paths of convergence of finitely dimensional (numerical and random) attractors towards the global attractor. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow model derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the interstitial avascular phase, both being mixed in the limit homogenised problem. When the vessel walls become more permeable, we show that the biphase fluid flow exhibits a boundary layer that make the computation of the full problem costly and unstable. In the limit, both capillary and interstitial pressures coincide except in the vicinity of the boundary where different boundary conditions are applied. Thanks to a rigorous asymptotic analysis, we prove that the solution to the full problem can be approached at any order of approximation by a monophasic model with appropriate boundary conditions on the tumor boundary and appropriate correcting terms near the boundary are given. Numerical simulations in spherical geometry illustrate the theoretical results. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Sufficient conditions characterizing the globally uniformly exponential stabilization of impulsive systems under two event-triggered impulsive control strategies are obtained. For the first strategy, the specific triggering condition is verified continuously, while for the second one that is discretely monitored. The second relied on a positive constant is the discrete-time version of the first one in order to reduce the computational burden. The analysis of the minimum time between two consecutive events for two control strategies is available in this paper. Moreover, the data dropout of impulsive control signals in event triggered condition is studied and the maximal permissible dropout rate is estimated under each strategy. An example and its simulation is given to demonstrate the results. (C) 2021 Elsevier Inc. All rights reserved.
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