Classifications and existence criteria for positive solutions of systems of nonlinear differential equations

Classification schemes for positive solutions of a class of second order nonlinear differential systems are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also provided.     

Cohen-Grossberg神经网络指数稳定性的新判则

避免构造Lyapunov函数的困难,运用广义Dahlquist数方法研究了Cohen- Grossberg神经网络模型的指数稳定性,不但得到了Cohen-Grossberg神经网络平衡点存在惟一性和指数稳定性的全新充分条件,而且给出了神经网络的指数衰减估计.与已有文献结果相比,所得的神经网络指数稳定的充分条件更为宽松,给出的解的指数衰减速度估计也更为精确.     

New existence results of positive solution for a class of nonlinear fractional differential equations

In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.     

On a new existence of equilibrium in SSC

In this note, we shall give a new existence theorem of equilibrium in social systems with coordination under general assumptions by using the Kakutani fixed point theorem.     

New stability criteria for neural networks with time-varying delays

This paper is concerned with the stability analysis problem of neural networks with time delays. The delay intervals [−d(t), 0] and [−h, 0] are divided into m subintervals with equal length. Some free matrices are introduced to build the relationship among the elements of the resultant matrix inequalities. With the above operations, the new stability criteria are built for the general class of neural networks. The conditions are presented in the form of linear matrix inequalities (LMIs), which can be solved by the numerically efficient Matlab LMI toolbox. Several examples are provided to show that our methods are much less conservative than recently reported ones.     

Characterization of the existence of a pure-strategy Nash equilibrium

In this work, we provide a necessary and sufficient condition for the existence of a pure-strategy Nash equilibrium for non-cooperative games in topological spaces.     

一个带毒生化反应竞争模型正平衡解的全局稳定性

研究两个微生物竞争同一营养,而其中一个竞争者会产生毒素抑制另一竞争者且产物系数γi(S)(i=1,2)为一般的非减可导函数时的生化反应模型,指出两篇文献中存在的问题,分析系统平衡点的稳定性,三维系统经历Hopf分支的条件和由此产生的周期解的稳定性.证明系统中某一微生物物种处于竞争劣势而趋于灭绝时另一微生物物种和营养在二维稳定流形上极限环的存在性.并用具体的实例验证文中所得结论.     

Coefficient criteria for the existence of a limit cycle in a two-dimensional system with hysteresis

Necessary and sufficient conditions for existence of a limit cycle in a two-dimensional system with hysteresis nonlinearity are derived in terms of the system coefficients.     

Eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second-order delay differential equations

Criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second-order delay differential equations of the form

     

An existence result for the generalized vector equilibrium problem

In this paper, we prove an existence result for the generalized vector equilibrium problem by using Fan-Browder type fixed-point theorem due to [1].     

New LMI-based criteria for global robust stability of delayed neural networks

Some novel, linear matrix inequality based, criteria for the uniqueness and global robust stability of the equilibrium point of Hopfield-type neural networks with delay are presented. A comparison of the present criteria with the previous criteria is made.     

New minimax inequality with applications to existence theorems of equilibrium points

A new minimax inequality is proved on a set which is the union of an increasing sequence of compact convex sets in a topological vector space. As applications, several existence theorems of equilibrium points for different games are obtained.The authors would like to thank the referees for their helpful suggestions.     

An existence theorem of equilibrium for generalized games in H-spaces

In this paper, we first prove a new fixed-point theorem from which the Kakutani's fixed-point theorem in locally convex topological vector spaces is immediately extended to H-spaces. Then, we establish a new existence theorem of equilibrium for generalized games in H-spaces, by applying our fixed-point theorem.     

On the existence of bounded positive solutions for a class of singular BVPs

We investigate the existence and properties of solutions to a second-order singular ODE. We base ourselves on the variational approach, which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences.     

On the existence of a walrasian equilibrium in a model of interregional economic relations

We establish rather general conditions for the existence of a Walrasian equilibrium in the interregional interaction models studied in a series of articles on multiregional economic systems. In contrast to the complicated technical assumptions of the previously announced existence theorem, the conditions here amount to simple modifications of the standard requirements of equilibrium analysis: the absence of regional ??cornucopia?? and strict autarchy of all participants of the model. Furthermore, strict autarchy is directly analogous to the well-known positivity conditions of initial supply for the classical exchange model. In addition to a proof of the main result we discuss its application to the comparative analysis of unblocking states and Walrasian and Edgeworthian equilibrium states of the multiregional economic systems under consideration.     

Univalent positive polynomial maps and the equilibrium state of chemical networks of reversible binding reactions

We consider a map given for x=(x₁,…,x_n) by

where I is a finite subset of , a_α is a constant in for each αI, and ψ₁,…,ψ_n are differentiable order-preserving functions . We prove that f is a bijection. Surjectivity arises as a consequence of the Brouwer Fixed-Point Theorem. For injectivity, we show that the Jacobian matrix of f is everywhere a P-matrix and we then apply the Gale–Nikaidô Global Univalence Theorem. With ψ₁==ψ_n=1, f is a positive polynomial map of interest in the study of chemical networks of reversible binding reactions. For these, we propose notions of elementary and composite species and of normal and complete networks. Many networks in pharmacology and other fields fall in these classes. We prove that their equilibrium states and detailed-balanced states coincide and are unique with respect to total concentrations of elementary species. The map f gives rise to an equation that has a unique solution which gives the equilibrium state. We also prove that concentrations always converge to the equilibrium state, thereby settling for complete networks the Global Attractor Conjecture, which affirms this property for the larger class of complex-balancing networks.