bifurcation analysis on a two neuron system with distributed delays abstract a general two neuron model with distributed delays is studied in this paper its local linear stability is analyzed by using the routh hurwitz criterion if the mean delay is used as a bifurcation parameter we prove that hopf bifurcation occurs for a weak kernel this means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value the direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical analysis are also given

entrainment control in a noisy neural system the open plus closed loop opcl entrainment control put forth by jackson and grosu physica d 85 1995 is applied to an effective neuron system as a way to extract stable limit cycles from a chaotic attractor analogous to the retrieval of memories from a memory searching state additive gaussian white noise representing the natural noise inherent in any real dynamical system is added to the entrainment control mechanism moderate levels of additive noise have little effect on successful entrainment as reflected in phase space plots and lyapunov exponents all three lyapunov exponents are negative which suggests parallels between opcl control and chaotic synchronization al 2

logarithmic lower bounds in the cell probe model we develop a new technique for proving cell probe lower bounds on dynamic data structures this technique enables us to prove an amortized randomized omega lg n lower bound per operation for several data structural problems on n elements including partial sums dynamic connectivity among disjoint paths or a forest or a graph and several other dynamic graph problems by simple reductions such a lower bound breaks a long standing barrier of omega lg n lg lg n for any dynamic language membership problem it also establishes the optimality of several existing data structures such as sleator and tarjan s dynamic trees we also prove the first omega log b n lower bound in the external memory model without assumptions on the data structure such as the comparison model our lower bounds also give a query update trade off curve matched e g by several data structures for dynamic connectivity in graphs we also prove matching upper and lower bounds for partial sums when parameterized by the word size and the maximum additive change in an update

two neuron dynamics and adiabatic elimination abstract we consider an effective neuron network obtained from the hopfield model by adiabatic elimination the validity of the slaving procedure is first numerically examined the self interaction of the effective neuron network may lead to non zero attractors far from the origin ui 0 the qualitative structure of the attractors for this two effective neuron model with j12j21 0 or

new amortized cell probe lower bounds for dynamic problems abstract we build upon the recent papers by weinstein and yu 11 larsen 7 and clifford et al 3 to present a general framework that gives amortized lower bounds on the update and query times of dynamic data structures using our framework we present two concrete results 1 for the dynamic polynomial evaluation problem where the polynomial is defined over a finite field of size n 1 1 and has degree n any dynamic data structure must either have an amortized update time of lg n lg lg n 2 or an amortized query time of lg n lg lg n 2 2 for the dynamic online matrix vector multiplication problem where we get an n n matrix whose entires are drawn from a finite field of size n 1 any dynamic data structure must either have an amortized update time of lg n lg lg n 2 or an amortized query time of n lg n lg lg n 2 for these two problems the previous works by larsen 7 and clifford et al 3 gave the same lower bounds but only for worst case update and query times our bounds match the highest unconditional lower bounds known till date for any dynamic problem in the cell probe model

on a class of left continuous t norms in this paper we study the subclass of left continuous t norms n which are definable by an arbitrary continuous t norm and a weak i e non necessarily involutive negation n by putting x n y 0 if x n y x n y x y otherwise thus generalizing the construction of the so called nilpotent minimum t norms we provide the characterization of weak negations compatible with a given continuous t norm and conversely which are the continuous t norms compatible with a given weak negation function

hopf bifurcation and stability for a delayed tri neuron network model a neural network model with three neurons and a single time delay is considered its linear stability is investigated and hopf bifurcations are demonstrated by analyzing the corresponding characteristic equation in particular the explicit formulae determining the stability and the direction of periodic solutions bifurcating from hopf bifurcations are obtained by applying the normal form theory and the center manifold theorem in order to illustrate our theoretical analysis some numerical simulations are also included in the end

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

synchronization and desynchronization in a network of locally coupled wilson cowan oscillators a network of wilson cowan wc oscillators is constructed and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis the network is a 2d matrix where each oscillator is coupled only to its neighbors we show analytically that a chain of locally coupled oscillators the piecewise linear approximation to the wc oscillator synchronizes and we present a technique to rapidly entrain finite numbers of oscillators the coupling strengths change on a fast time scale based on a hebbian rule a global separator is introduced which receives input from and sends feedback to each oscillator in the matrix the global separator is used to desynchronize different oscillator groups unlike many other models the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding gestalt principles of feature grouping the ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure ground segregation based on oscillatory correlation

hopf bifurcation of an n 1 neuron bidirectional associative memory neural network model with delays recent studies on hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two three four five or six neurons it is well known that neural networks are complex and large scale nonlinear dynamical systems so the dynamics of the delayed neural networks are very rich and complicated although discussing the dynamics of networks with a few neurons may help us to understand large scale networks there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large scale networks in this paper a general delayed bidirectional associative memory neural network model with n 1 neurons is considered by analyzing the associated characteristic equation the local stability of the trivial steady state is examined and then the existence of the hopf bifurcation at the trivial steady state is established by applying the normal form theory and the center manifold reduction explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution furthermore the paper highlights situations where the hopf bifurcations are particularly critical in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections it is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons numerical simulations are carried out to illustrate the main results

duration of transient oscillations in ring networks of unidirectionally coupled neurons abstract properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network the duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons the distribution of the duration is approximated by a power law function when the number of neurons is large further transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases

a study of network dynamics the dynamics of a discrete time neural network model are investigated first a numerical survey of network power spectra is reported for networks of varying size with random weight matrices and initial states the steepness of the logistic function and a symmetry measure of the weight matrix are taken as control parameters summary statistics are presented to give gross measures of the model s temporal activity in parameter space second a detailed study of the dynamics of a particular network is described complex dynamical behavior is observed including hopf bifurcations the ruelle takens newhouse route to chaos showing mode locking at rational winding numbers and the destruction of an invariant torus and the period doubling route to chaos

delay induced periodicity in a neural netlet of excitation and inhibition abstract the dynamical behaviour of a two neuron netlet of excitation and inhibition with a transmission delay is investigated it is shown that in the absence of delay the netlet relaxes to the trivial resting state if the delay is of sufficient magnitude the network is excited to a temporally periodic cyclic behaviour the analytical mechanism for the onset of cyclic behaviour is through a hopf type bifurcation approximate solusions to the periodic output of the netlet is calculated stability of the temporally periodic cycle is investigated it is shown that the bifurcation is supercritical a related discrete version of the continuous time system is formulated it is found that the discrete system also displays a cyclic behaviour results of a number of computer simulations are displayed graphically the article concludes with a brief neurobiological discussion

on good eq algebras a special algebra called eq algebra has been recently introduced by vilem novak its original motivation comes from fuzzy type theory in which the main connective is fuzzy equality eq algebras have three binary operations meet multiplication and fuzzy equality and a unit element they open the door to an alternative development of fuzzy many valued logic with the basic connective being a fuzzy equality instead of an implication this direction is justified by the idea presented by g w leibniz that a fully satisfactory logical calculus must be an equational one in this paper we continue the study of eq algebras and their special cases we introduce and study the prefilters and filters of separated eq algebras we give great importance to the study of good eq algebras as we shall see in this paper the goodness property and thus separateness is necessary for reasonably behaving algebras we enrich good eq algebras with a unary operation d the so called baaz delta fulfilling some additional assumptions that are heavily used in fuzzy logic literature we show that the characterization theorem obtained until now for representable good eq algebras also hold for the enriched algebra

effect of delay on the boundary of the basin of attraction in a self excited single graded response neuron little attention has been paid in the past to the effects of interunit transmission delays representing a xonal and synaptic delays ontheboundary of the basin of attraction of stable equilibrium points in neural networks as a first step toward a better understanding of the influence of delay we study the dynamics of a single graded response neuron with a delayed excitatory self connection the behavior of this system is representative of that of a family of networks composed of graded response neurons in which most trajectories converge to stable equilibrium points for any delay value it is shown that changing the delay modifies the location of the boundary of the basin of attraction of the stable equilibrium points without affecting the stability of the equilibria the dynamics of trajectories on the boundary are also delay dependent and influence the transient regime of trajectories within the adjacent basins our results suggest that when dealing with networks with delay it is important to stud

on v filters and normal v filters of a residuated lattice with a weak vt operator in this paper we study further the filter theory of residuated lattices first we discuss the concepts of filters and normal filters of residuated lattices and propose some equivalent conditions for them then we introduce and investigate the notions of v filter and normal v filter of a residuated lattice with a weak vt operator and lay bare the formulas for calculating the v filters and the normal v filters generated by subsets finally we show that the lattices of v filters and normal v filters of a residuated lattice with a vt operator are both complete brouwerian lattices

bifurcation and stabilization of oscillations in ring neural networks with inertia effects of inertia on oscillations in ring networks of unidirectionally coupled sigmoidal neurons are studied it is known that ring neural networks without inertia are bistable and the duration of transient oscillations increases exponentially with the number of neurons in this paper a kinematical description of traveling waves in the oscillations in the networks is extended to networks with inertia when the inertia is below a critical value and the state of each neuron is over damped properties of the networks are qualitatively the same as those without inertia the duration of the transient oscillations then increases with inertia and the increasing rate of the logarithm of the duration becomes more than double when the inertia exceeds a critical value and the state of each neuron becomes under damped properties of the networks qualitatively change the periodic solution is then stabilized through the pitchfork bifurcation as inertia increases more bifurcations occur so that various periodic solutions are generated and the stability of the periodic solutions changes alternately further stable oscillations generated with inertia are observed in an experiment on an analog circuit

nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb abstract a mathematical model of the process of pattern recognition in the first olfactory sensory cortex of the rabbit is presented it explains the formation and alteration of spatial patterns in neural activity observed experimentally during classical pavlovian conditioning on each inspiration of the animal a surge of receptor input enters the olfactory bulb eeg activity recorded at the surface of the bulb undergoes a transition from a low amplitude background state of temporal disorder to coherent oscillation there is a distinctive spatial pattern of rms amplitude in this oscillation which changes reliably to a second pattern during each successful recognition by the animal of a conditioned stimulus odor when a new odor is paired as conditioned stimulus these patterns are replaced by new patterns that stabilize as the animal adapts to the new environment i will argue that a unification of the theories of pattern formation and associative memory is required to account for these observations this is achieved in a model of the bulb as a discrete excitable medium with spatially inhomogeneous coupling expressed by a connection matrix the theory of multiple hopf bifurcations is employed to find coupled equations for the amplitudes of competing unstable oscillatory modes these may be created in the system by proper coupling and selectively evoked by specific classes of inputs this allows a view of limit cycle attractors as stored fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory

product units a computationally powerful and biologically plausible extension to backpropagation networks we introduce a new form of computational unit for feedforward learning networks of the backpropagation type instead of calculating a weighted sum this unit calculates a weighted product where each input is raised to a power determined by a variable weight such a unit can learn an arbitrary polynomial term which would then feed into higher level standard summing units we show how learning operates with product units provide examples to show their efficiency for various types of problems and argue that they naturally extend the family of theoretical feedforward net structures there is a plausible neurobiological interpretation for one interesting configuration of product and summing units

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

computing hopf bifurcations i this paper addresses the problems of detecting hopf bifurcations in systems of ordinary differential equations and following curves of hopf points in two parameter families of vector fields the established approach to this problem relies upon augmenting the equilibrium condition so that a hopf bifurcation occurs at an isolated regular point of the extended system we propose two new methods of this type based on classical algebraic results regarding the roots of polynomial equations and properties of kronecker products for matrices in addition to their utility as augmented systems for use with standard newton type continuation methods they are also particularly well adapted for solution by computer algebra techniques for vector fields of small or moderate dimension

fuzzy rough sets based on generalized residuated lattices this paper is devoted to propose generalized l fuzzy rough sets as a further generalization of the notion of l fuzzy rough sets a quadruple of approximation operators are defined to suit the situation when generalized residuated lattices are non commutative generalized l fuzzy rough sets are characterized from both constructive and axiomatic approaches in the constructive approach various classes of generalized l fuzzy rough sets are investigated moreover the relationship between generalized l fuzzy rough sets and l topologies on an arbitrary universe is discussed with generalized lower and upper sets as an application of generalized l fuzzy rough sets fuzzy rough sets are proposed and studied on the unit interval 0 1 which are based on generalized residuated lattices induced by left continuous pseudo t norms

periodic entrainment of chaotic logistic map dynamics consider the map dynamics xn 1 f xn c with a control parameter c let the governing set gn n 0 1 2 be a desired periodic dynamic set gn n gn it is noted that the non autonomous system xn 1 f xn c gn has such a solution xn gn if gn gn 1 f gn c in particular the set of values gn38 might be obtained from the periodic solutions of gn 1 f gn c using suitable values of c this study explores the values of c which yield entrained solutions their basin of entrainment x0 limn xn gn 0 and more generally the basins of bounded solutio ns and their character when f x c cx 1 x the logistic map of particular interest is the entrainment of chaotic dynamics c 4 generally the basin of entrainment for period one governing g0 is x0 1 g0 1 c g0 1 c 2c with the above b asin or if c 1 2c g0 c 4 2c with the basin x 0 g0 x0 1 g0 the complimentary x0 region yields unbounded dynamics period two governing values have two basins depending on the initial value used for g0 these basins are investigated for the sets gn 1 f gn c other periodic sets gn in gn do not become disjoint i n space period four entrainment for suitable c can have even larger basins the unwanted occurrence of other disjoint basins of attraction which interlace the basins of entrainment as a function of both x0 and g0 is discussed other periodic and non periodic responses to these periodic gn are also studied

stability and chaos in an inertial two neuron system abstract inertia is added to a continuous time hopfield 1984 effective neuron system we explore the effects on the stability of the fixed points of the system a two neuron system with one or two inertial terms added is shown to exhibit chaos the chaos is confirmed by lyapunov exponents power spectra and phase space plots

global robust stability of neural networks with time varying delays in this paper we study the global robust stability of neural networks with time varying delays using the lyapunov functional method and matrix inequality technique several sufficient conditions are presented to show the existence of equilibrium and global robust stability of neural networks which is easy to apply then we give a simulation to justify the obtained results

entrainment and migration controls of two dimensional maps a general approach to several types of controls of complex dynamic systems formulated by jackson is applied to two classic two dimensional maps xk 1 e xk x r2 the henon and the ikeda maps the convergent regions of their phase spaces ck are shown to respectively possess translational and rotatational symmetries several topologically distinct entrainment goals e goals gk ck are illustrated for the henon map for both maps the basins of entrainment be g0 x0 limk xk g0 0 of the controlled dynamics for fixed point goals in each convergent region g0 ck are illustrated the be g0 are invariant relative to g0 when g0 is varied by the above symmetries it is proved that for the ikeda map be g0 0 r2 for experimental purposes spheres of entrainment are introduced se r0 x0 x0 g0 r g0 where r g0 maxr r x0 g0 r limk xk g0 0 the ikeda map has two attractors in a bounded region so that migration controls can be illustrated this is done using several migration goals m goals which transfer this system from one attractor to the basin of attraction of the other attractor a1 ba2 or a2 ba1 these require controls only for finite times the influence of noise on the entrainment process is analyzed and compared with numerical examples

symmetries and pattern selection in rayleigh benard convection abstract this paper describes the process of pattern selection between rolls and hexagons in rayleigh benard convection with reflectional symmetry in the horizontal midplane this symmetry is a consequence of the boussinesq approximation provided the boundary conditions are the same on the top and bottom plates all possible local bifurcation diagrams assuming certain non degeneracy conditions are found using only group theory the results are therefore applicable to other systems with the same symmetries rolls hexagons or a new solution regular triangles can be stable depending on the physical system rolls are stable in ordinary rayleigh benard convection the results are compared to those of buzano and golubitsky 1 without the midplane reflection symmetry the bifurcation behavior of the two cases is quite different and a connection between them is established by considering the effects of breaking the reflectional symmetry finally the relevant experimental results are described

mean square exponential stability of stochastic inertial neural networks by introducing some parameters perturbed by white noises we propose a class of stochastic inertial neural networks in random environments to describe dynamics behaviours of this stochastic system

dynamics of simple electronic neural networks abstract we examine systems of one and two nonlinear threshold switching elements neurons of the kind used in electronic neural networks characteristics of these systems which deviate from standard ideal models are found to induce complex dynamics when the neurons possess a finite frequency response or a transfer characteristic with a time delay underdamped transients and instability leading to oscillation can occur inertia in the neuron connections is found to cause ringing about fixed points convoluted basin boundaries instability and spontaneous oscillation and chaotic behavior when driven furthermore the collective behavior of a network of multiple neurons can be underdamped even when the individual connections are overdamped these results imply that care should be exercised in implementing networks with electronic devices or when adding inertia to enhance the performance of optimizing networks

non commutative fuzzy structures and pairs of weak negations abstract weak pseudo bl algebras wpbl algebras are non commutative fuzzy structures which arise from pseudo t norms i e the non commutative versions of triangular norms in this paper we study the pairs of weak negations on wpbl algebras extending the case of weak negations on esteva godo mtl algebras a geometrical characterization of the pairs of weak negations in bounded chains is provided our main result characterizes the pairs of weak negations compatible with the multiplication of totally ordered wpbl algebras giving a way to obtain new examples of wpbl algebras we use this to identify all the compatible pairs of weak negations on finite mv chains

stability and hopf bifurcation analysis on a simplified bam neural network with delays a delay differential equation modelling a bidirectional associative memory bam neural network with three neurons is investigated its dynamics are studied in terms of local analysis and hopf bifurcation analysis by analyzing the associated characteristic equation its linear stability is investigated and hopf bifurcations are demonstrated the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold reduction numerical simulation results are given to support the theoretical predictions

nonlinear dynamics and symbolic dynamics of neural networks a piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks a symbolic representation of the dynamics in this equation is given as a directed graph on an n dimensional hypercube this provides a formal link with discrete neural networks such as the original hopfield models analytic criteria are given to establish steady states and limit cycle oscillations independent of network dimension model networks that display multiple stable limit cycles and chaotic dynamics are discussed the results show that such equations are a useful and efficient method of investigating the behavior of neural networks

stochastic single neurons we study the stochastic behavior of a single self exciting model neuron with additive noise a system that has bistable stochastic dynamics we use langevin and fokker planck equations to obtain analytical expressions for the stationary distribution of activities and for the crossing rate between two stable states we adjust the parameters in these expressions to fit observed histograms of neural activity thus obtaining what we call an effective single neuron for a given network we construct an effective single neuron from an activity histogram of a representative hidden neuron in a recurrent learning network we also compare our result with an effective single neuron previously obtained analytically through the adiabatic elimination approximation

pattern segmentation in associative memory the goal of this paper is to show how to modify associative memory such that it can discriminate several stored patterns in a composite input and represent them simultaneously segmention of patterns takes place in the temporal domain components of one pattern becoming temporally correlated with each other and anticorrelated with the components of all other patterns correlations are created naturally by the usual associative connections in our simulations temporal patterns take the form of oscillatory bursts of activity model oscillators consist of pairs of local cell populations connected appropriately transition of activity from one pattern to another is induced by delayed self inhibition or simply by noise

variational calculation of the limit cycle and its frequency in a two neuron model with delay we consider a model system of two coupled hopfield neurons which is described by delay differential equations taking into account the finite signal propagation and processing times when the delay exceeds a critical value a limit cycle emerges via a supercritical hopf bifurcation first we calculate its frequency and trajectory perturbatively by applying the poincar e lindstedt method then the perturbation series are resummed by means of the shohat expansion in good agreement with numerical values however with increasing delay the accuracy of the results from the shohat expansion worsens we thus apply variational perturbation theory vpt to the perturbation expansions to obtain more accurate results which moreover hold even in the limit of large delays

hopfield net generation encoding and classification of temporal trajectories hopfield network transient dynamics have been exploited for resolving both path planning and temporal pattern classification for these problems lagrangian techniques and two well known learning algorithms for recurrent networks have been used for path planning the williams and zisper s learning algorithm has been implemented and a set of temporal trajectories which join two points pass through others avoid obstacles and jointly form the shortest path possible are discovered and encoded in the weights of the net the temporal pattern classification is based on an extension of the pearlmutter s algorithm for the generation of temporal patterns which is obtained by means of variational methods the algorithm is applied to a simple problem of recognizing five temporal trajectories with satisfactory robustness to distortions

an open plus closed loop opcl control of complex dynamic systems a new method of contmlfing arbitrary nonlinear dynamic systems dx dt f x t x c n is presented it is proved that there exists solutions x t in the neighborhood of any arbitrary goal dynamics g t that are entrained to g t through the use of an additive controlling action k g x t h dg dt g c g t g t x which is the sum of the openloop h ibler action h dg dt g and a suitable linear closed lo0p feedback action c g t examples of some newly obtained entrainment capabilities are given for the during and van der pol systems for these and the lorenz and rtssler systems proofs are given for global basins of entrainment for all goal dynamics that can be exponentially bounded in time the basin of entrainment is also established for the chua system as well as the possibility of a coexisting basin of attraction to another fixed point

bifurcation and category learning in network models of oscilating cortex abstract a genetic model of oscillating cortex which assumes minimal coupling justified by known anatomy is shown to function as an associative memory using previously developed theory the network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long range excitatory connections using a local hebb like learning rule for primary and higher order synapses at the ends of the long range connections the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex in olfaction these patterns emerge during respiration by a pattern forming phase transition which we characterize in the model as a multiple hopf bifurcation we argue that these bifurcations play an important role in the operation of real digital computers and neural networks and we use bifurcation theory to derive learning rules which analytically guarantee cam storage of continuous periodic sequences capacity n 2 fourier components for an n node network no spurious attractors

should tables be sorted we examine optimality questions in the following information retrieval problem given a set s of n keys store them so that queries of the form is x in s can be answered quickly it is shown that in a rather general model including al1 the commonly used schemes lceil lg n l rceil probes to the table are needed in the worst case provided the key space is sufficiently large the effects of smaller key space and arbitrary encoding are also explored

towards a comprehensive theory of brain activity coupled oscillator systems under external forces abstract recently jirsa et al and haken discussed a theory comprising the brain wave equation proposed by nunez the wilson cowan ermentrout cowan model and hopfield networks this theory was applied to model findings obtained in an experiment that relates brain activity and behavior the so called julliard experiment in previous works of jirsa et al and frank et al the focus was on the brain wave aspect recently we conducted similar experiments the results obtained are modeled in this paper in terms of coupled oscillator systems coupled oscillator systems are considered to represent the wilson cowan ermentrout cowan model aspect of the unifying theory building on a model proposed by haken kelso and bunz and the theory of weakly coupled oscillators established by winfree and by kuramoto we derive a nonlinear fokker planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments

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

temporal coding assembly formation through constructive interference temporal coding is studied for an oscillatory neural network model with synchronization and acceleration the latter mechanism refers to increasing decreasing the phase velocity of each unit for stronger weaker or more coherent decoherent input from the other units it has been demonstrated that acceleration generates the desynchronization that is needed for self organized segmentation of two overlapping patterns in this letter we continue the discussion of this remarkable feature giving also an example with several overlapping patterns due to acceleration hebbian memory implies a frequency spectrum for pure pattern states defined as coherent patterns with decoherent overlapping patterns with reference to this frequency spectrum and related frequency bands the process of pattern retrieval corresponding to the formation of temporal coding assemblies is described as resulting from constructive interference with frequency differences due to acceleration and phase locking due to synchronization

parameter space structure of continuous time recurrent neural networks a fundamental challenge for any general theory of neural circuits is how to characterize the structure of the space of all possible circuits over a given model neuron as a first step in this direction this letter begins a systematic study of the global parameter space structure of continuous time recurrent neural networks ctrnns a class of neural models that is simple but dynamically universal first we explicitly compute the local bifurcation manifolds of ctrnns we then visualize the structure of these manifolds in net input space for small circuits these visualizations reveal a set of extremal saddle node bifurcation manifolds that divide ctrnn parameter space into regions of dynamics with different effective dimensionality next we completely characterize the combinatorics and geometry of an asymptotically exact approximation to these regions for circuits of arbitrary size finally we show how these regions can be used to calculate estimates of the probability of encountering different kinds of dynamics in ctrnn parameter space

pseudo bl algebras and pseudo effect algebras pseudo bl algebras and pseudo effect algebras arose in two rather different fields fuzzy logics and quantum logics in this paper by introducing the notion of pseudo weak mv effect algebra which is non commutative generalization of weak mv effect algebra we investigate the mutual relationship between pseudo bl algebras and pseudo effect algebras we prove that dual pseudo bl algebra under certain condition can be restricted to a pseudo weak mv effect algebra and a pseudo weak mv effect algebra can be extended to dual pseudo bl algebra under certain condition moreover we give some examples of pseudo bl algebra which is corresponding to some pseudo weak mv effect algebra finally we establish the relationship between pseudo mv algebras and pseudo mv effect algebras

on the control of complex dynamic systems a method is described for the limited control of the dynamics of systems which generally have several dynamic attractors associated either with maps or first order ordinary differential equations ode in rn the control is based on the existence of convergent regions cc k 1 2 in the phase space of such systems where there is local convergence of all nearby orbits the character of the control involves the entrainment and subsequent possible migration of the experimental system from one attractor to another entrainment means that limt x t g t 0 where x t rn is the system s controlled dynamics and the goal dynamics g t gk has any topological form but is limited dynamically and to regions of phase space gk contained in some ck gk ck the control process is initiated only when the system enters a basin of entrainment bek gk associated with the goal region gk aside from this macroscopic initial state information about the system no further feedback of dynamic information concerning the response of the system is required the experimental reliability of the control requires that the regions bek be convex regions in the phase space which can apparently be assured if gk ck simple illustrations of these concepts are given using a general linear and a piecewise linear ode in rn in addition to these entrainment goals migration goal dynamics is introduced which intersects two convergent regions g cj g cj i j and permits transferring the dynamics of a system from one attractor to another or from one convergent region to another in the present study these concepts are illustrated with various one dimensional maps involving one or more attractors and convergent regions several theorems concerning entrainment are derived for very general continuous one dimensional maps sufficient conditions are also established which ensure near entrainment for a system when the dynamic model of the system is not exactly known the applications of these concepts to higher dimensional maps and flows will be presented in subsequent studies

analysis of continuous time switching networks abstract models of a number of biological systems including gene regulation and neural networks can be formulated as switching networks in which the interactions between the variables depend strongly on thresholds an idealized class of such networks in which the switching takes the form of heaviside step functions but variables still change continuously in time has been proposed as a useful simplification to gain analytic insight these networks called here glass networks after their originator are simple enough mathematically to allow significant analysis without restricting the range of dynamics found in analogous smooth systems a number of results have been obtained before particularly regarding existence and stability of periodic orbits in such networks but important cases were not considered here we present a coherent method of analysis that summarizes previous work and fills in some of the gaps as well as including some new results furthermore we apply this analysis to a number of examples including surprising long and complex limit cycles involving sequences of hundreds of threshold transitions finally we show how the above methods can be extended to investigate aperiodic behaviour in specific networks though a complete analysis will have to await new results in matrix theory and symbolic dynamics

adjoint negations more than residuated negations negation operators are useful operators which have extensively been studied and used in different fuzzy settings such as in fuzzy logic this paper introduces a new and flexible kind of negation operator based on adjoint triples and which is called adjoint negation relative to a fixed element besides proving several interesting properties the comparison with weak negations studied by trillas esteva et al and pairs of weak negations introduced by georgescu and popescu is presented furthermore adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor

a bifurcation analysis of the four dimensional generalized hopfield neural network abstract a four neuron hopfield neural network with asymmetric weights and self connection is analyzed its stable steady state and periodic attractors are identified and a complete bifurcation diagram is constructed a center manifold reduction is undertaken and by means of normal form theory the characteristics of the limit cycles are obtained the network is seen to have a large memory storage capacity with both fixed point and periodic memories coexisting the onset of chaos as reported previously is considered

boolean filters and positive implicative filters of residuated lattices the aim of this paper is to introduce the notions of boolean filters and positive implicative filters in residuated lattices and to investigate their properties several characterizations of boolean filters and positive implicative filters are derived the extension theorems of implicative filters and positive implicative filters are obtained the relations among boolean filters implicative filters and positive implicative filters are investigated and it is proved that boolean filters are equivalent to implicative filters and that every boolean filter is a positive implicative filter but the converse may not be true furthermore the conditions under which a positive implicative filter is a boolean filter are established

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

algorithms for controlling chaotic motion application for the bvp oscillator the bvp oscillator is a biologically and physically important dynamical system exhibiting chaotic motion phaselocking phenomenon and so on in this paper we investigate the controlling of chaos in this system both when periodic and constant currents are present we use the various control algorithms and investigate their effectiveness in particular we study the controlling by the following mechanisms i adaptive control algorithm ii weak periodic perturbations iii ott grebogi yorke method iv weak feedback control and v addition of noise also we show the suppression of chaos by numerical models

global competition and local cooperation in a network of neural oscillators abstract an architecture of locally excitatory globally inhibitory oscillator networks is proposed and investigated both analytically and by computer simulation the model for each oscillator corresponds to a standard relaxation oscillator with two time scales oscillators are locally coupled by a scheme that resembles excitatory synaptic coupling and each oscillator also inhibits other oscillators through a common inhibitor oscillators are driven to be oscillatory by external stimulation the network exhibits a mechanism of selective gating whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern while preventing the other oscillators from jumping up we show analytically that with the selective gating mechanism the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks computer simulations demonstrate the model s promising ability for segmenting multiple input patterns in real time this model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure ground segregation

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

amplitude equations for systems with competing instabilities we describe how to derive ordinary differential equations to predict the time dependence of a system governed by partial differential equations when that system is near to the polycritical condition for the onset of several instabilities the method is illustrated for the general case of two competing instabilities and then a specific physical example of this case is worked out in detail the basic idea is to extend the krylov bogolyubov mitropolsky method of nonlinear mechanics to bifurcation problems