global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays in this paper we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays sufficient conditions are derived for ascertaining the existence uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method the periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays

finite time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller this paper is concerned about the finite time stabilizability and instabilizability for a class of delayed memristive neural networks dmnns through the design of a new nonlinear controller algebraic criteria based on m matrix are established for the finite time stabilizability of dmnns and the upper bound of the settling time for stabilization is estimated in addition finite time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller the effectiveness and the superiority of the obtained results are supported by numerical simulations

global asymptotic stability analysis of discrete time cohen grossberg neural networks based on interval systems abstract the global asymptotic stability of discrete time cohen grossberg neural networks cgnns with or without time delays is studied in this paper the cgnns are transformed into discrete time interval systems and several sufficient conditions for asymptotic stability for these interval systems are derived by constructing some suitable lyapunov functionals the conditions obtained are given in the form of linear matrix inequalities that can be checked numerically and very efficiently by using the matlab lmi control toolbox finally some illustrative numerical examples are provided to demonstrate the effectiveness of the results obtained

an improved algebraic criterion for global exponential stability of recurrent neural networks with time varying delays this brief paper presents an m matrix based algebraic criterion for the global exponential stability of a class of recurrent neural networks with decreasing time varying delays the criterion improves some previous criteria based on m matrix and is easy to be verified with the connection weights of the recurrent neural networks with decreasing time varying delays in addition the rate of exponential convergence can be estimated via a simple computation based on the criterion herein

uniform stability of fractional order leaky integrator echo state neural network with multiple time delays abstract this paper deals with the uniform stability of the fractional order leaky integrator echo state neural network foesn with multiple delays the delays occur in the transmission the readout and the leakage of the network and have constant values sufficient conditions for uniform intrinsical stability of such networks in the presence of delays are provided the intrinsical stability guarantees the foesn is stable independently of the delays in addition the existence and uniqueness of the equilibrium point using the contraction mapping theorem are derived simulation results illustrate the effectiveness of the proposed method

global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the paper presents theoretical results on the global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the dynamic analysis in the paper employs the theory of differential equations with discontinuous right hand side as introduced by filippov by using the inequality techniques and a useful lyapunov functional some new testable algebraic criteria are obtained for ensuring the existence and global exponential stability of periodic solution of the system the model based on the memristor widens the application scope for the design of neural networks and the new effective results also enrich the toolbox for the qualitative analysis of neural networks

global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling this paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays a novel coupling scheme is introduced in a general topological structure described by a directed or undirected graph with a linear diffusive term and discontinuous sign term several criteria are derived based on the lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme simulation results for several examples are given to substantiate the effectiveness of the theoretical results

dissipativity analysis of memristor based complex valued neural networks with time varying delays in this paper the problem of dissipativity analysis for memristor based complex valued neural networks mcvnns with time varying delays is investigated extensively dissipativity analysis is an important concept in control system theory and its applications the analysis in the paper employ results from the theory of differential equations with discontinuous right hand side as introduced by filippov by using the framework of filippov solution differential inclusion theory an appropriate lyapunov krasovskii functional and linear matrix inequality lmi technique several new sufficient conditions for global dissipativity global exponential dissipativity and strictly q s r dissipativity are derived in the form of complex valued as well as real valued lmis both real and complex valued lmis guarantee feasibility results for addressed mcvnns these lmis can be solved by using standard available numerical packages moreover the global attractive sets which are positive invariant are obtained finally three numerical examples are established to illustrate the effectiveness of the proposed theoretical results

highly transitive imprimitivities abstract some new observations are made about imprimitive permutation groups associated with subfactors of von neuman algebras of particular interest are examples of a group g containing two maximal subgroups h and k such that g h k and such that the action of g on the space of cosets of h k has small rank few suborbits the rank 6 case turns out to correspond to the action of the collineation group on flags of a desarguesian projective plane and a special case of interest for rank 7 corresponds to the action of a 4 transitive group on ordered pairs of distinct points some other new and unexpected fundamental properties of groups are described along the way

on intervals in subgroup lattices of finite groups we investigate the question of which finite lattices l are isomorphic to the lattice h g of all overgroups of a subgroup h in a finite group g we show that the structure of g is highly restricted if h g is disconnected we define the notion of a signalizer lattice in h and show for suitable disconnected lattices l if h g is minimal subject to being isomorphic to l or its dual then either g is almost simple or h admits a signalizer lattice isomorphic to l or its dual we use this theory to answer a question in functional analysis raised by watatani

global µ stability criteria for quaternion valued neural networks with unbounded time varying delays in this paper we first propose quaternion valued neural networks qvnns with unbounded time varying delays some sufficient conditions on the global stability in the form of both complex valued and real valued linear matrix inequalities lmis are provided by solving two difficulties one is decomposing the qvnn into two complex valued systems with the plural decomposition method of quaternion which can reduce the complexity of calculations by avoiding the non commutativity of quaternion multiplication the other is choosing the appropriate lyapunov krasovskii functional in the form of hermitian matrices which is a big challenge finally two numerical examples are provided to verify the effectiveness of the obtained results

novel delay dependent stability criterion for time varying delay systems with parameter uncertainties and nonlinear perturbations this study proposes a novel approach to obtain less conservative conditions for the robust stability analysis for time varying delay systems with parameter uncertainties and nonlinear perturbations specifically first we divide the time varying delay into non uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms more exactly second novel delay derivation dependent stability criteria are derived by introducing a parameter c in the lyapunov krasovskii functional third we define some new variables to deal with uncertain parameters finally two numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results

periodic solutions for semi linear evolution inclusions in this paper we study the periodic problem for semi linear evolution inclusion using techniques from multivalued analysis and fixed point theorems we establish existence theorems under the one sided lipschitz condition first we prove existence theorems for nonconvex and convex problem second we look for extremal periodic solutions and prove the relaxation theorem

passivity and passification of memristor based recurrent neural networks with additive time varying delays this paper presents a new design scheme for the passivity and passification of a class of memristor based recurrent neural networks mrnns with additive time varying delays the predictable assumptions on the boundedness and lipschitz continuity of activation functions are formulated the systems considered here are based on a different time delay model suggested recently which includes additive time varying delay components in the state the connection between the time varying delay and its upper bound is considered when estimating the upper bound of the derivative of lyapunov functional it is recognized that the passivity condition can be expressed in a linear matrix inequality lmi format and by using characteristic function method for state feedback passification it is verified that it is apathetic to use immediate or delayed state feedback by constructing a lyapunov krasovskii functional and employing jensen s inequality and reciprocal convex combination technique together with a tighter estimation of the upper bound of the cross product terms derived from the derivatives of the lyapunov functional less conventional delay dependent passivity criteria are established in terms of lmis moreover second order reciprocally convex approach is employed for deriving the upper bound for terms with inverses of squared convex parameters the model based on the memristor with additive time varying delays widens the application scope for the design of neural networks finally pertinent examples are given to show the advantages of the derived passivity criteria and the significant improvement of the theoretical approaches

a novel neural network for solving semidefinite programming problems with some applications abstract in this paper we present a neural network model for solving semidefinite programming we show that the equilibrium point of the proposed neural network and the kkt point of the semidefinite programming are equal by employing lyapunov function approach it is also shown that the suggested neural network model is stable in the sense of lyapunov and globally convergent to an exact optimal solution of the original problem some applications of the proposed scheme are stated by modeling of some important problems as semidefinite programming problems numerical simulations verify the obtained theoretical results

lattices of intermediate subfactors letnbe an irreducible subfactor of a typeii1factorm if the jones index m n is finite then the set lat n m of the intermediate subfactors for the inclusionn mforms afinitelattice the commuting and co commuting square conditions for intermediate subfactors are related to the modular identity in the lattice lat n n in particular simplicity of a finite groupgis characterized in terms of commuting square conditions of intermediate subfactors forn m n g we investigate the question of which finite lattices can be realized as intermediate subfactor lattices

global exponential stability and global convergence in finite time of delayed neural networks with infinite gain this paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections and neuron activations belonging to the set of discontinuous monotone increasing and possibly unbounded functions the discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity while the delay accounts for the finite switching speed of the neuron amplifiers or the finite signal propagation speed it is known that the delay in combination with high gain nonlinearities is a particularly harmful source of potential instability the goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay more precisely conditions are given under which there is a unique equilibrium point of the neural network which is globally exponentially stable for the states with a known convergence rate the conditions are easily testable and independent of the delay moreover global convergence in finite time of the state and output is investigated in doing so new interesting dynamical phenomena are highlighted with respect to the case without delay which make the study of convergence in finite time significantly more difficult the obtained results extend previous work on global stability of delayed neural networks with lipschitz continuous neuron activations and neural networks with discontinuous neuron activations but without delays

on the periodic dynamics of memristor based neural networks with time varying delays abstract in this paper we study the existence uniqueness and stability of periodic solution for a wide class of memristor based neural networks with time varying delays by employing the topological degree theory in set valued analysis differential inclusions theory and a new lyapunov function method we prove that the neural network has a unique periodic solution which is globally exponentially stable moreover we prove the existence uniqueness and global exponential stability of equilibrium point for time varying delayed memristor based neural networks with constant coefficients the obtained results improve and extend previous works on memristor based or usual neural network dynamical systems with continuous or discontinuous right hand side finally two numerical examples are provided to show the applicability and effectiveness of our main results

attractivity analysis of memristor based cellular neural networks with time varying delays this paper presents new theoretical results on the invariance and attractivity of memristor based cellular neural networks mcnns with time varying delays first sufficient conditions to assure the boundedness and global attractivity of the networks are derived using state space decomposition and some analytic techniques it is shown that the number of equilibria located in the saturation regions of the piecewise linear activation functions of an n neuron mcnn with time varying delays increases significantly from 2n to 22n2 n 22n2 times compared with that without a memristor in addition sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived finally two illustrative examples are given to elaborate the characteristics of the results in detail

quantum subgroups of the haagerup fusion categories we answer three related questions concerning the haagerup subfactor and its even parts the haagerup fusion categories namely we find all simple module categories over each of the haagerup fusion categories in other words we find the quantum subgroups in the sense of ocneanu we find all irreducible subfactors whose principal even part is one of the haagerup fusion categories and we compute the brauer picard groupoid of morita equivalences of the haagerup fusion categories in addition to the two even parts of the haagerup subfactor there is exactly one more fusion category which is morita equivalent to each of them this third fusion category has six simple objects and the same fusion rules as one of the even parts of the haagerup subfactor but has not previously appeared in the literature we also find the full lattice of intermediate subfactors for every irreducible subfactor whose even part is one of these three fusion categories and we discuss how our results generalize to izumi subfactors

a novel neural network model for solving a class of nonlinear semidefinite programming problems abstract in this paper we describe a dynamic optimization technique for solving a class of nonlinear semidefinite programming based on karush kuhn tucker optimality conditions by employing lyapunov function approach it is investigated that the suggested neural network is stable in the sense of lyapunov and globally convergent to an exact optimal solution of the original problem the effectiveness of the proposed method is demonstrated by two numerical simulations

generalized lyapunov approach for convergence of neural networks with discontinuous or non lipschitz activations the paper considers a class of additive neural networks where the neuron activations are modeled by discontinuous functions or by continuous non lipschitz functions some tools are developed which enable us to apply a lyapunov like approach to differential equations with discontinuous right hand side modeling the neural network dynamics the tools include a chain rule for computing the time derivative along the neural network solutions of a nondifferentiable lyapunov function and a comparison principle for this time derivative which yields conditions for exponential convergence or convergence in finite time by means of the lyapunov like approach a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions moreover new results on global convergence in finite time are established which are applicable to neuron activations with jump discontinuities or neuron activations modeled by means of continuous non lipschitz holder functions

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

finite time stabilization of delayed memristive neural networks discontinuous state feedback and adaptive control approach in this paper a general class of delayed memristive neural networks dmnns system described by functional differential equation with discontinuous right hand side is considered under the extended filippov framework we investigate the finite time stabilization problem for dmnns by using the famous finite time stability theorem and the generalized lyapunov functional method to do so we design two classes of novel controllers including discontinuous state feedback controller and discontinuous adaptive controller without assuming the boundedness and monotonicity of the activation functions several sufficient conditions are given to stabilize the states of this class of dmnns in finite time moreover the upper bounds of the settling time for stabilization are estimated finally numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results

passivity and passification of memristor based recurrent neural networks with time varying delays this paper presents new theoretical results on the passivity and passification of a class of memristor based recurrent neural networks mrnns with time varying delays the casual assumptions on the boundedness and lipschitz continuity of neuronal activation functions are relaxed by constructing appropriate lyapunov krasovskii functionals and using the characteristic function technique passivity conditions are cast in the form of linear matrix inequalities lmis which can be checked numerically using an lmi toolbox based on these conditions two procedures for designing passification controllers are proposed which guarantee that mrnns with time varying delays are passive finally two illustrative examples are presented to show the characteristics of the main results in detail

on a subfactor generalization of wallʼs conjecture abstract in this paper we discuss a conjecture on intermediate subfactors which is a generalization of wall s conjecture from the theory of finite groups we explore special cases of this conjecture and present supporting evidence in particular we prove special cases of this conjecture related to some finite dimensional kac algebras of izumi kosaki type which include relative version of wall s conjecture for solvable groups