共查询到20条相似文献,搜索用时 15 毫秒
1.
The dynamical behavior of a delayed neural network with bi-directional coupling is investigated by taking the delay as the
bifurcating parameter. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using
the theory of functional differential equations. As the propagation time delay in the coupling varies, stability switches
for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined
by applying the normal form theory and the center manifold theorem. We also discuss the spatio-temporal patterns of bifurcating
periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation
theory of Lie groups. In particular, we obtain that the spatio-temporal patterns of bifurcating periodic oscillations will
alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond
to different patterns of neural activities. Numerical simulations are given to illustrate the obtained results and show the
existence of bursts in some interval of the time for large enough delay. 相似文献
2.
Harold J. Kushner 《Applied Mathematics and Optimization》2010,62(3):295-322
We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the
dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the
problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems
via use of the averaged equation. 相似文献
3.
G. van der Laan A. J. J. Talman Z. Yang 《Journal of Optimization Theory and Applications》2010,144(2):391-407
Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set
{±1,±2,…,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits
a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite
set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1,±2,…,±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some
mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0,1}
n
+q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations
under certain natural conditions. An economic application is provided. 相似文献
4.
We present a general method for constructing stochastic processes with prescribed local form, encompassing examples such as
variable amplitude multifractional Brownian and multifractional α-stable processes. We apply the method to Poisson sums to construct multistable processes, that is, processes that are locally
α(t)-stable but where the stability index α(t) varies with t. In particular we construct multifractional multistable processes, where both the local self-similarity and stability indices
vary. 相似文献
5.
In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi.
Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan’s congruences for the unrestricted
partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0,
pod(32a+3n+\frac23×32a+2+18) o 0 (mod 3).\mathrm{pod}\biggl(3^{2\alpha+3}n+\frac{23\times3^{2\alpha+2}+1}{8}\biggr)\equiv 0\ (\mathrm{mod}\ 3). 相似文献
6.
We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability
problems of electrodynamic space tethers. Both static (buckling) and dynamic (whirling) instability are considered and we
also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling
of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse
anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary
solutions, we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers
and potentially for future applications in nano- and molecular wires. 相似文献
7.
Mihai Popescu 《Journal of Applied Mathematics and Computing》2008,27(1-2):393-409
We consider the controlled systems where the non-linear term is multiplied by a small scalar parameter ε. In the class of these quasi-linear systems, we shall determine the control and optimal trajectory which minimizes the index of performance represented by quadratics functionals. The initial and final conditions are specified and the final time is free. The presence of the small parameter leads to an approximate solution of the formulated problem of optimum. Thus, the zeroth-order solution is obtained for ε=0. The first order solution results by using the sweep method which determines the perturbation of the control and of the state variable on the optimal neighboring trajectory. 相似文献
8.
Paweł Bechler 《Journal of Fourier Analysis and Applications》2009,15(1):31-57
Let BV
r
denote the space of distributions f such that the distributional derivatives D
α
f with |α|≤r exist as measures of bounded variation. This paper discusses estimates for wavelet coefficients of BV
r
distributions, direct (Jackson) and inverse (Bernstein) inequalities for n-term approximation of elements of BV
r
in the L
p
spaces using compactly supported wavelets. In particular, optimal rates of approximation are established. Linear approximation
in similar contexts is also considered for comparison.
This research was supported by the 2003–2007 Academic Grant of Prof. P. Wojtaszczyk awarded by the Foundation for Polish Science.
Part of this research was supported within the HASSIP framework. 相似文献
9.
Transient solutions for M/M/c queues are important for staffing call centers, police stations, hospitals and similar institutions. In this paper we show how to find transient solutions for M/M/c queues with finite buffers by using eigenvalues and eigenvectors. To find the eigenvalues, we create a system of difference equations where the coefficients depend on a parameter x. These difference equations allow us to search for all eigenvalues by changing x. To facilitate the search, we use Sturm sequences for locating the eigenvalues. We also show that the resulting method is numerically stable. 相似文献
10.
Marco Rocco 《Set-Valued and Variational Analysis》2011,19(3):457-485
In the framework of real Banach spaces, the present paper provides a necessary and sufficient condition for the Fitzpatrick
function of the subdifferential of a proper lower semicontinuous convex function to be autoconjugate. This enables us to:
obtain a new proof of the fact that subdifferentials of indicator and sublinear functions have autoconjugate Fitzpatrick functions;
characterize those classes of functions whose subdifferentials fulfill the condition under study in the same special way as
indicator and sublinear functions do; prove that, in the one-dimensional case, the functions of these classes are the only
ones whose subdifferentials have autoconjugate Fitzpatrick functions, while this is not true in higher dimensions. 相似文献
11.
Xiangyun Shi Xueyong Zhou Xinyu Song 《Journal of Applied Mathematics and Computing》2010,33(1-2):305-325
In this paper, the dynamical behavior of an eco-epidemiological model with discrete and distributed delay is studied. Sufficient conditions for the local asymptotical stability of the nonnegative equilibria are obtained. We prove that there exists a threshold value of the feedback time delay τ beyond which the positive equilibrium bifurcates towards a periodic solution. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions. 相似文献
12.
Douglas R. Anderson Richard I. Avery 《Journal of Applied Mathematics and Computing》2011,37(1-2):297-312
Green’s functions for new second-order periodic differential and difference equations with variable potentials are found, then used as kernels in integral operators to guarantee the existence of a positive periodic solution to continuous and discrete second-order periodic boundary value problems with periodic coefficient functions. A new version of the Leggett-Williams fixed point theorem is employed. 相似文献
13.
In this paper, we first consider difference equations with several delays in the neutral term of the form
14.
D. Sadhukhan L. N. Sahoo B. Mondal M. Maiti 《Journal of Applied Mathematics and Computing》2010,34(1-2):1-18
A multispecies harvesting model with mutual interactions is formulated based on Lotka–Voltera model with three competing species which are affected not only by harvesting but also by the presence of prey, predator and the third species, which is super predator. In order to understand the dynamics of the system, it is assumed that the super predator follows the logistic growth. Further, there is demand for all the above three species in the market and hence harvesting of all species is performed. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin’s maximal principle. Finally some numerical examples are discussed to illustrate the model. 相似文献
15.
We introduce variational inequalities defined in non-pivot Hilbert spaces and we show some existence results. Then, we prove
regularity results for weighted variational inequalities in non-pivot Hilbert space. These results have been applied to the
weighted traffic equilibrium problem. The continuity of the traffic equilibrium solution allows us to present a numerical
method to solve the weighted variational inequality that expresses the problem. In particular, we extend the Solodov-Svaiter
algorithm to the variational inequalities defined in finite-dimensional non-pivot Hilbert spaces. Then, by means of a interpolation,
we construct the solution of the weighted variational inequality defined in a infinite-dimensional space. Moreover, we present
a convergence analysis of the method. 相似文献
16.
This paper aims to establish duality and exact penalization results for the primal problem of minimizing an extended real-valued
function in a reflexive Banach space in terms of a valley-at-0 augmented Lagrangian function. It is shown that every weak
limit point of a sequence of optimal solutions generated by the valley-at-0 augmented Lagrangian problems is a solution of
the original problem. A zero duality gap property and an exact penalization representation between the primal problem and
the valley-at-0 augmented Lagrangian dual problem are obtained. These results are then applied to an inequality and equality
constrained optimization problem in infinite-dimensional spaces and variational problems in Sobolev spaces, respectively.
The first author was supported by the Research Committee of Hong Kong Polytechnic University, by Grant 10571174 from the National
Natural Science Foundation of China and Grant 08KJB11009 from the Jiangsu Education Committee of China.
The second author was supported by Grant BQ771 from the Research Grants Council of Hong Kong.
We are grateful to the referees for useful suggestions which have contributed to the final presentation of the paper. 相似文献
17.
The infinite horizon risk-sensitive control problem for non-degenerate controlled diffusions is analyzed under a ‘near monotonicity’
condition on the running cost that penalizes large excursions of the process. 相似文献
18.
We introduce a class of ordered monoids defined by the existence of certain “unique products” with respect to artinian and
narrow subsets of the monoid. The logical relationships between this and other significant classes of monoids are explicated
with several examples. We conclude with results on skew generalized power series rings. The new class of monoids provides
the appropriate setting for obtaining results on reduced rings and domains of skew generalized power series, and on analogues
of Armendariz rings. 相似文献
19.
We establish boundedness properties on products of weighted Lebesgue, Hardy, and amalgam spaces of certain paraproducts and
bilinear pseudodifferential operators with mild regularity. We do so by showing that these operators can be realized as generalized
bilinear Calderón–Zygmund operators.
相似文献
20.
Rade T. Živaljević 《Discrete and Computational Geometry》2009,41(1):135-161
This paper lays the foundation for a theory of combinatorial groupoids that allows us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature”, etc. in the context
of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. We introduce a new, holonomy-type
invariant for cubical complexes, leading to a combinatorial “Theorema Egregium” for cubical complexes that are non-embeddable
into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool to extend Babson–Kozlov–Lovász graph coloring results to more general statements about
nondegenerate maps (colorings) of simplicial complexes and graphs.
The author was supported by grants 144014 and 144026 of the Serbian Ministry of Science and Technology. 相似文献
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