hamiltonian formulation of a theory with constraints the hamiltonian formulation of a constrained dynamical system with four degrees of freedom the quantization of which has recently been discussed by hojman and shepley j math phys 32 142 1991 is considered the theory possesses four primary constraints which are all second class the system is quantized using the dirac s procedure next the theory is reduced to the three dimensional one by setting q4 k const it is found that the theory now possesses only three primary constraints which are all first class and consequently the theory now becomes a gauge theory this three dimensional theory is then quantized using the dirac s procedure again under different gauge fixing conditions

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

global stability analysis in delayed cellular neural networks in this paper the author analyzes further problems of global stability for a class of cellular neural networks with delays by means of the lyapunov functional method inequalities a 2 b 2 g 2ab and a 3 b 3 c 3 g 3abc a b cg 0 analysis technique some stability criteria are obtained under more general conditions these criteria can be applied to design globally stable networks and thus have important significance in both theory and applications

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

stability analyses of cellular neural networks with continuous time delay the stability of cellular neural networks cnns with continuous time delay is investigated in the present paper a main theorem together with a few corollaries related to the existence and boundedness of the solution for this kind of cnns as well as its global asymptotic stability is derived some numerical simulation examples aimed at justifying the theoretical results are also given

involution and constrained dynamics ii the faddeev jackiw approach for pt i see seiler et al ibid vol 28 p 4431 1995 we study the symplectic approach to first order systems with constraints from the point of view of the formal theory of differential equations we concentrate especially on systems without first class constraints and give a geometric interpretation of an approach recently proposed by barcelos neto and wotzasek 1992 we further study the numerical properties of this approach we also comment on some problems concerning the application to field theories

robust stability analysis for interval cohen grossberg neural networks with unknown time varying delays in this paper robust stability problems for interval cohen grossberg neural networks with unknown time varying delays are investigated using linear matrix inequality m matrix theory and halanay inequality techniques new sufficient conditions independent of time varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval cohen grossberg neural networks with time varying delays all these results have no restriction on the rate of change of the time varying delays compared to some existing results these new criteria are less conservative and are more convenient to check two numerical examples are used to show the effectiveness of the present results

on the nature of the gardner transformation it is shown that every higher korteveg de vries equation can be included in a one parameter family of integrable equations

new exponential stability results for delayed neural networks with time varying delays abstract this paper presents new sufficient conditions for the uniqueness and exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a more general type of lyapunov krasovskii functional and using lmi linear matrix inequality we derive new results for exponential stability of the equilibrium point for delayed neural networks the results establish a relation between the delay time and the parameters of the network the results are compared with the previous results derived in the literature

absolute exponential stability of recurrent neural networks with generalized activation function in this paper the recurrent neural networks rnns with a generalized activation function class is proposed in this proposed model every component of the neuron s activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space all of the convex hulls are composed of generalized activation function classes the novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes the absolute exponential stability aest of the rnn with a generalized activation function class is studied through three steps the first step is to demonstrate the global exponential stability ges of the equilibrium point of original rnn with a generalized activation function being equivalent to that of rnn under all vertex functions of convex hull the second step transforms the rnn under every vertex activation function into neural networks under an array of saturated linear activation functions because the ges of the equilibrium point of three systems are equivalent the next stability analysis focuses on the ges of the equilibrium point of rnn system under an array of saturated linear activation functions the last step is to study both the existence of equilibrium point and the ges of the rnn under saturated linear activation functions using the theory of m matrix in the end a two neuron rnn with a generalized activation function is constructed to show the effectiveness of our results

stability analysis of distributed delay neural networks based on relaxed lyapunov krasovskii functionals this paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays the distributed delays are assumed to be constant and prescribed since a positive definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite it is important for constructing relaxed lyapunov krasovskii functionals which generally lead to less conservative stability criteria based on this fact and using two kinds of integral inequalities a new delay dependent condition is obtained which ensures that the distributed delay neural network under consideration is globally asymptotically stable this stability criterion is then improved by applying the delay partitioning technique two numerical examples are provided to demonstrate the advantage of the presented stability criteria

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

the construction of a poisson structure out of a symmetry and a conservation law of a dynamical system a method to construct hamiltonian theories for systems of both ordinary and partial differential equations is presented the knowledge of a lagrangian is not at all necessary to achieve the result the only ingredients required for the construction are one solution of the symmetry perturbation equation and one constant of motion of the original system it turns out that the poisson bracket structure for the dynamical variables is far from becoming uniquely determined by the differential equations of motion examples in classical mechanics as well as in field theory are presented

no lagrangian no quantization this work starts with classical equations of motion and sets very general quantization conditions commutation relations it is proved that these conditions imply that the equations of motion are equivalent to the euler lagrange equations of a lagrangian l the result is a generalization of work by feynman recently reported by dyson am j phys 58 209 211 1990 the lagrangian l need not be unique examples are given including classical equations that do not come from a lagrangian and therefore cannot be quantized consistently

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

comment on hamiltonian formulation of a theory with constraints u kulshreshta j math phys 33 633 1992 the hamiltonian formulation of a constrained dynamical system analyzed by kulshreshta j math phys 33 633 1992 is discussed the theory possesses four coordinates and four primary second class constraints and thus two physical degrees of freedom the correct equations of motion for the system are given the reduced theory q4 k is shown to have three primary and one secondary second class constraints instead of three primary first class ones as claimed by kulshreshta the equations of motion are derived using the dirac bracket

singular symmetries of integrable curves and surfaces if w w x t is a solution of wt 6wwx wxxx 6e2w2wx then w e 2 is also a solution in general integrable families and their members admit discrete symmetries whereas original systems may not

an analysis of global asymptotic stability of delayed cellular neural networks in this paper a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks dcnns this condition imposes constraints on the feedback and delayed feedback matrices of a dcnn independently of the delay parameter this result is also compared with the previous results derived in the literature

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

symmetries of lagrangians and of their equations of motion a new kind of lagrangian symmetry is defined in such a way that the resulting set of lagrangian symmetries coincides with the set of symmetries of its equations of motion several constants of motion may be associated to each of the new symmetry transformations one example is presented

quantization of non standard hamiltonian systems the quantization of classical theories that admit more than one hamiltonian description is considered this is done from a geometrical viewpoint both at the quantization level geometric quantization and at the level of the dynamics of the quantum theory a spin system is taken as an example in which all the steps can be completed it is shown that the geometry of the quantum theory imposes restrictions on the physically allowed non standard quantum theories

specializations of integrable systems and affine lie algebras we analyze a number of restrictions on the evolution systems associated with the zero curvature equations corresponding to the extended dynkin diagram a 1 n 1 the resulting specialized evolution systems contain exponential terms like a third order differential equation previously derived in ref 5

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

stability analysis of discrete time recurrent neural networks with stochastic delay this paper is concerned with the stability analysis of discrete time recurrent neural networks rnns with time delays as random variables drawn from some probability distribution by introducing the variation probability of the time delay a common delayed discrete time rnn system is transformed into one with stochastic parameters improved conditions for the mean square stability of these systems are obtained by employing new lyapunov functions and novel techniques are used to achieve delay dependence the merit of the proposed conditions lies in its reduced conservatism which is made possible by considering not only the range of the time delays but also the variation probability distribution a numerical example is provided to show the advantages of the proposed conditions

global stability for cellular neural networks with time delay a sufficient condition related to the existence of a unique equilibrium point and its global asymptotic stability for cellular network networks with delay dcnns is derived it is shown that the condition relies on the feedback matrices and is independent of the delay parameter furthermore this condition is less restrictive than that given in the literature

the helmholtz conditions in terms of constants of motion in classical mechanics the helmholtz conditions are the necessary and sufficient conditions for a set of second order differential equations to be equivalent to a variational principle in this work an alternative approach to the inverse problem in classical mechanics is described it is proven that the helmholtz conditions can be transformed into a set of conditions for a nonsingular antisymmetric matrix whose entries are constants of motion of the problem in question

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

a generalized lmi based approach to the global asymptotic stability of delayed cellular neural networks a novel linear matrix inequality lmi based criterion for the global asymptotic stability and uniqueness of the equilibrium point of a class of delayed cellular neural networks cnns is presented the criterion turns out to be a generalization and improvement over some previous criteria

on the inverse problem of the calculus of variations we consider the inverse problem of the calculus of variations for any system by writing its differential equations of motion in first order form we provide a way of constructing infinitely many lagrangians for such a system in terms of its constants of motion using a covariant geometrical approach we present examples of first order lagrangians for systems for which no second order lagrangians exist the hamiltonian theory for first order degenerate lagrangians is constructed using dirac s method for singular lagrangians

stability and dissipativity analysis of distributed delay cellular neural networks in this brief the problems of delay dependent stability analysis and strict q s dissipativity analysis are investigated for cellular neural networks cnns with distributed delay first by introducing an integral partitioning technique two new forms of lyapunov krasovskii functionals are constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities based on this criterion a new sufficient delay and dependent condition is given to guarantee that the cnns with distributed delay are strictly q s dissipative the results developed in this brief can tolerate larger allowable delay than existing ones in the literature which is demonstrated by several examples

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme