noncommutative fiber products and lattice models abstract we establish a connection between the representation theory of certain noncommutative singular varieties and two dimensional lattice models specifically we consider noncommutative biparametric deformations of the fiber product of two kleinian singularities of type a special examples are closely related to the schrodinger algebra s 1 the affine lie algebra a 1 1 and a finite w algebra associated to sl 4 the algebras depend on two scalars and two polynomials that must satisfy the mazorchuk turowska equation mte which we re interpret as a quantization of the ice rule local current conservation in statistical mechanics solutions to the mte previously classified by the author and d rosso can accordingly be expressed in terms of multisets of higher spin vertex configurations on a twisted cylinder we first reduce the problem of describing the category of weight modules to the case of a single configuration l secondly we classify all simple weight modules over the corresponding algebras a l in terms of the connected components of the cylinder minus l lastly we prove that a l are crystalline graded rings as defined by nauwelaerts and van oystaeyen and describe the center of a l explicitly in terms of l along the way we prove several new results about twisted generalized weyl algebras and their simple weight modules

the liapunov dimension of strange attractors abstract many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange in this paper the question of estimating the dimension of the attractor is addressed while more general conjectures are made here particular attention is paid to the idea that if the jacobian determinant of a map is greater than one and a ball is mapped into itself then generically the attractor will have positive two dimensional measure and most of this paper is devoted to presenting cases with such jacobians for which the attractors are proved to have non empty interior

dynamical complexity detection in short term physiological series using base scale entropy physiological systems generate complex fluctuations in their output signals that reflect the underlying dynamics the base scale entropy method was proposed as a complexity measure to investigate the complexity of time series the advantages of this method are simplicity and extremely fast calculation for very short data sets this method enables analyzing very short nonstationary and noisy data sets we employed this method for short term physiological time series for analysis of heart rate variability signals the results show that the simple and easily calculated measure can effectively detect the complexity dissimilarity of physiological time series in different physiological or pathological states which is convenient for clinical applications

a class of initials dependent dynamical systems the dynamics of initial dependent system is investigated the potential mechanism for initial dependent property is discussed general scheme is proposed to design initial dependent dynamical system this scheme can be used for chaos control by initial setting with memristor nonlinear term is critical for emergence of chaos in autonomous dynamical systems the sampled time series in chaotic system are dependent on the initial selection of variables while the attractors are invariant for fixed parameters in this paper the dynamical behavior of a class of dynamical system is investigated at fixed parameter region it is found that the state selection is dependent on the initials and the potential mechanism is discussed it is confirmed that the system can be switched between stable state periodical state and even chaotic state by selecting appropriate initials even the parameters are fixed we think that nonlinear cross terms with higher order could account for the emergence of this behavior it indicates that initial selection and resetting can be also effective to control some chaotic systems and these chaotic systems could enhance security for possible secure communication because the chaotic attractor depends on the parameter and initials selection as well in the case of secure communication the reconstruction of phase space becomes more difficult because the attractors are changed arbitrarily thus the safety for secure keys is enhanced for chaos control when the initials are reset the controller can be removed and the system can develop to step into the desired target by itself

locally finite simple weight modules over twisted generalized weyl algebras abstract we present methods and explicit formulas for describing simple weight modules over twisted generalized weyl algebras when a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification of a class of locally finite simple weight modules as those induced from simple modules over a subalgebra isomorphic to a tensor product of noncommutative tori as an application we describe simple weight modules over the quantized weyl algebra

a class of algebras similar to the enveloping algebra of sl 2 fix f e c x define r c a b h subject to the relations ha ah a hb bh b ab ba f h we study these algebras for different f and in particular show how they are similar to and different from u sl 2 the enveloping algebra of sl 2 c there is a notion of highest weight modules and a category a for such r for each n 0 if f x x 1 n l xn 1 then r has precisely n simple modules in each finite dimension and every finite dimensional r module is semisimple

response of nonlinear oscillators with random frequency of excitation revisited periodically driven oscillators of low frequency random excitations are analyzed computer simulation which was carried out for the duffing equation and forced vibrations of a pendulum indicated that in these cases noise has a stabilizing effect computation of lyapunov exponents showed that by adding noise to chaotic motion the largest lyapunov exponent as a rule turns to negative and consequently the chaotic motion is annihilated

moment lyapunov exponents of a two dimensional system under combined harmonic and real noise excitations abstract the moment lyapunov exponents and the lyapunov exponents of a two dimensional system under combined excitations of harmonic and real noise which is modelled as an ornstein uhlenbeck process are studied the moment lyapunov exponents and the lyapunov exponents are important characteristics determining the moment and almost sure stability of a stochastic dynamical system the eigenvalue problem governing the moment lyapunov exponent is established a regular perturbation method is applied to solve the eigenvalue problem to obtain second order weak noise expansions of the moment lyapunov exponents the influence of the real noise excitation on the parametric resonance due to the harmonic excitation is investigated

analysis and stabilization of nonlinear chaotic systems the qualitative analysis problem for chaotic dynamics of nonlinear control systems and stabilization of unstable periodic orbits upo stabilization and stationary states were considered in the paper nonlinear control systems are analysed by the canonical transformation methods of affine systems and by the localization of periodic orbits method based on properties of lie derivatives along smooth vector fields it is proved that lorenz and rossler systems are not equivalent in the affine classification for chaotic systems a general approach to upo stabilization and stabilization of stationary states based on canonical transformations was proposed estimates for chaotic regions in the phase space for lorenz and rossler systems were obtained relations between canonical transformations localization and upo stabilization problems were studied

remote synchronization in star networks we study phase synchronization in a network motif with a starlike structure in which the central node s the hub s frequency is strongly detuned against the other peripheral nodes we find numerically and experimentally a regime of remote synchronization rs where the peripheral nodes form a phase synchronized cluster while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes we explain the mechanism for this rs by the existence of a free amplitude and also show that systems with a fixed or constant amplitude such as the classic kuramoto phase oscillator are not able to generate this phenomenon further we derive an analytic expression which supports our explanation of the mechanism

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

observations of order and chaos in nonlinear systems experiments on nonlinear electrical oscillators the belousov zhabotinskii reaction rayleigh benard convection and couette taylor flow have revealed several common routes to chaos that have also been found in numerical studies of models with a few degrees of freedom experimental results are presented illustrating the following transition sequences period doubling and the u sequence intermittency the periodic quasiperiodic chaotic sequence frequency locking and an alternating periodic chaotic sequence

recurrence plot analysis of irregularly sampled data irregularly sampled time series usually require data preprocessing before a desired time series analysis can be applied we propose an approach for distance measuring of pairs of data points which is directly applicable to irregularly sampled time series in order to apply recurrence plot analysis to irregularly sampled time series we use this approach and detect regime transitions in prototypical models and for an application from palaeoclimatatology this approach might be useful for any method that is based on distance measuring e g correlation sum or lyapunov exponent estimation

chaos in a variable mass relaxation oscillator model for the leaky tap abstract a variable mass relaxation oscillator model for the behaviour of the leaky tap is numerically investigated different regions of its three dimensional parameter space have been searched and interesting dynamical behaviour has been found the dynamics of the system is thoroughly characterized using projections of phase space trajectories 2 and 3 dimensional time delay plots power spectra lyapunov exponents hausdorff and correlation dimensions and bifurcation diagrams dynamical variables obtained from the model like drop masses velocities and drip intervals are used for reconstructing attractors we found several periodic intermittent and chaotic attractors we conclude that the rich dynamics of the model investigated represents an improvement in describing the experimentally observed behaviour of the actual dripping faucet system

solution of a q difference noether problem and the quantum gelfand kirillov conjecture for mathfrak gl _n it is shown that the q difference noether problem for all classical weyl groups has a positive solution simultaneously generalizing well known results on multisymmetric functions of mattuck proc am math soc 19 764 765 1968 and miyata nagoya math j 41 69 73 1971 in the case q 1 and q deforming the noncommutative noether problem for the symmetric group futorny et al in adv math 223 773 796 2010 it is also shown that the quantum gelfand kirillov conjecture for mathfrak gl n for a generic q follows from the positive solution of the q difference noether problem for the weyl group of type d n the proof is based on the theory of galois rings futorny and ovsienko in j algebra 324 598 630 2010 from here we obtain a proof of the quantum gelfand kirillov conjecture for mathfrak gl n and for a certain extension of mathfrak sl n previously the case of mathfrak sl n was shown by fauquant millet j algebra 218 93 116 1999 and by alev and dumas j algebra 170 229 265 1994 for n 2 3 moreover we give an explicit description of the skew fields of fractions for u q mathfrak gl n and u q mathrm ext mathfrak sl n which generalizes the results of alev and dumas j algebra 170 229 265 1994

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

localization of flexural waves in a disordered periodic piezoelectric beam abstract localization of bending waves in a disordered periodic piezoelectric beam is studied in this paper the equation of the wave motion for a piezoelectric beam is derived on the assumption of an euler bernoulli beam and the harmonic solution is presented the transfer matrix between two consecutive unit cells in the structures is obtained by using the continuity conditions the expression of the localization factor is given by wolf s algorithm numerical examples are presented and the effects of several disordered parameters on the localization factor are analyzed the results show that piezoelectricity has obvious effects on the passbands and stopbands of the periodic piezoelectric beam the behavior of wave propagation and localization in disordered periodic piezoelectric beams can be altered by tuning different structural parameters

analysis adaptive control and circuit simulation of a novel nonlinear finance system in the last three decades a growing interest in developing nonlinear dynamical systems for economic models displaying chaotic behavior has been developed to this direction a novel 3 d nonlinear finance chaotic system consisting of two nonlinearities is presented the dynamical analysis of the proposed system confirms its complex dynamic behavior which is studied by using well known simulation tools of nonlinear theory such as the bifurcation diagram lyapunov exponents and phase portraits also some interesting phenomena related with nonlinear theory are observed such as route to chaos through a period doubling sequence antimonotonicity and crisis phenomena in addition an interesting scheme of adaptive control of finance system s behavior is presented furthermore the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package cadence orcad in order to confirm the feasibility of the theoretical model

non linear dynamical system theory and primary visual cortical processing abstract the vertebrate brain consists of a large number of neurons each with highly complex non linear dynamics these neurons communicate with each other with a complex nexus of connecting nerve axons the current work examines the dynamical properties of neurons located in cat primary visual cortex from the perspective of non linear dynamical theory the temporal patterns of activation of such neurons achieved with periodic stimuli suggest that the dynamics are relatively simple and may be modeled using a small set of coupled non linear equations predictions are made based as to the patterns of activation to be found in populations of neurons

synchronization of chaotic orbits the effect of a finite time step two chaotic orbits can be synchronized by driving one of them by the other some of the variables of the driven orbit are set continuously to the corresponding variables of the drive orbit it has been seen that synchronization can be achieved if the subsystem lyapunov exponents corresponding to the remaining or response variables are all negative we find that a procedure where the drive variable is set at discrete times can also achieve synchronization however the synchronization criterion is altered by the effect of the drive being set at finite time steps an important consequence of this is found in the lorenz system where synchronization can be achieved with z as the drive variable despite the existence of a marginal subsystem lyapunov exponent we also find that synchronization can be achieved for the rossler attractor with z as the drive even though the largest subsystem lyapunov exponent is positive in addition we find that there is an optimal time step corresponding to the fastest rate of convergence for both cases above our synchronization criterion reduces to the usual subsystem lyapunov exponent criterion in the limit of the time step tending to zero

multiparameter twisted weyl algebras abstract we introduce a new family of twisted generalized weyl algebras called multiparameter twisted weyl algebras for which we parametrize all simple quotients of a certain kind both jordan s simple localization of the multiparameter quantized weyl algebra and hayashi s q analog of the weyl algebra are special cases of this construction we classify all simple weight modules over any multiparameter twisted weyl algebra extending results by benkart and ondrus we also describe all whittaker pairs up to isomorphism over a class of twisted generalized weyl algebras which includes the multiparameter twisted weyl algebras

experimental robust synchronization of hyperchaotic circuits abstract even if complete synchronization between two chaotic circuits can be reached only when the systems are identical in this paper we address the robustness of synchronization in the presence of parameter mismatches between the coupled circuits in the case of hyperchaotic behavior in particular a master slave scheme based on negative feedback t kapitaniak synchronization of chaos using continuous control phys rev e 50 1994 1642 1644 is considered and the strategy to design the slave system as an observer of the master is given with the proposed approach based on the concept of the master stability function the two circuits are coupled through a unique scalar signal experimental results obtained from two hyperchaotic circuits will be presented in order to show that synchronization occurs widely in the range of electronic component tolerances

classification of twisted generalized weyl algebras over polynomial rings abstract let r be a polynomial ring in m variables over a field of characteristic zero we classify all rank n twisted generalized weyl algebras over r up to z n graded isomorphisms in terms of higher spin 6 vertex configurations examples of such algebras include infinite dimensional primitive quotients of u g where g gl n sl n or sp 2 n algebras related to u sl 2 and a finite w algebra associated to sl 4 to accomplish this classification we first show that the problem is equivalent to classifying solutions to the binary and ternary consistency equations secondly we show that the latter problem can be reduced to the case n 2 which can be solved using methods from previous work by the authors 17 15 as a consequence we obtain the surprising fact that in the setting of the present paper the ternary consistency relation follows from the binary consistency relation

experiments on node to node pinning control of chua s circuits abstract in this paper we study the global intermittent pinning controllability of networks of coupled chaotic oscillators we explore the feasibility of the recently presented node to node pinning control strategy through experiments on chua s circuits we focus on the case of two peer to peer coupled chua s circuits and we build a novel test bed platform comprised of three inductorless chua s oscillators we investigate the effect of a variety of design parameters on synchronization performance including the coupling strength between the oscillators the control gains and the switching frequency of node to node pinning control experimental results demonstrate the effectiveness of this novel pinning control strategy in rapidly taming chaotic oscillator dynamics onto desired reference trajectories while minimizing the overall control effort and the number of pinned network sites from an analytical standpoint we present sufficient conditions for global node to node pinning controllability and we estimate the maximum switching period for network controllability by adapting and integrating available results on lyapunov stability theory and partial averaging techniques

simplicity and maximal commutative subalgebras of twisted generalized weyl algebras in this paper we prove three theorems about twisted generalized weyl algebras tgwas first we show that each non zero ideal of a tgwa has non zero intersection with the centralizer of the distinguished subalgebra r this is analogous to earlier results known to hold for crystalline graded rings second we give necessary and sufficient conditions for the centralizer of r to be commutative hence maximal commutative generalizing a result by v mazorchuk and l turowska and third we generalize results by d a jordan and v bavula on generalized weyl algebras by giving necessary and sufficient conditions for certain tgwas to be simple in the case when r is commutative we illustrate our theorems by considering some special classes of tgwas and providing concrete examples we also discuss how simplicity of a tgwa is related to the maximal commutativity of r and the non existence of non trivial z n invariant ideals of r less

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

route to hyperchaos in a system of coupled oscillators with multistability this work presents the results of a detailed experimental study into the transition between synchronized low dimensional and unsynchronized high dimensional dynamics using a system of coupled electronic chaotic oscillators novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets these originate from initially multistable low dimensional attractors which experience a smooth transition from low to high dimensional chaotic behavior losing stability through a bubbling bifurcation numerical techniques were also employed to verify and expand on the experimental results giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor this particular route to hyperchaos also results in the possibility of phenomena such as unstable dimension variability that can be a major obstruction to shadowing and predictability in chaotic systems

separation and synchronization of piecewise linear chaotic systems in this paper a topic regarding the synchronization of chaotic systems is dealt with the case of separation and synchronization of many chaotic signals generated by different chaotic circuits and combined together is examined in particular an observer based strategy has been adopted and an approach for the simultaneous stabilization of many luenberger observers has been investigated to face the problem of separation and synchronization the design strategy is based on linear matrix inequalities lmis indeed the lmi problem is referred to have a solution if a dual optimization problem admits a solution in our case the feasibility condition if it does exist allows us to establish that the separation and synchronization problem for the chosen circuit admits a solution some numerical simulations are reported further results refer to an experimental circuit showing the suitability of the approach furthermore the use of the proposed scheme to transmit two or more information masked into two or more multiplexed chaotic signals and the design of suitable parameters through the introduced technique based on lmis are discussed

symbolic dynamics of noisy chaos abstract one model of randomness observed in physical systems is that low dimensional deterministic chaotic attractors underly the observations a phenomenological theory of chaotic dynamics requires an accounting of the information flow from the observed system to the observer the amount of information available in observations and just how this information affects predictions of the system s future behavior in an effort to develop such a description we discuss the information theory of highly discretized observations of random behavior metric entropy and topological entropy are well defined invariant measures of such an attractor s level of chaos and are computable using symbolic dynamics real physical systems that display low dimensional dynamics are however inevitably coupled to high dimensional randomless e g thermal noise we investigate the effects of such fluctuations coupled to deterministic chaotic systems in particular the metric entropy s response to the fluctuations we find that the entropy increases with a power law in the noise level and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory we also argue that in addition to the metric entropy there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations i0 the maximum average information obtainable about the initial condition that produces a particular sequence of measurements or symbols

observation of a strange attractor abstract phase space portraits have been constructed and analyzed for noisy nonperiodic data obtained in an experiment on a nonequilibrium homogeneous chemical reaction the phase space trajectories define a limit set that is an attractor following a perturbation the trajectory quickly returns to the attracting set this attracting set is shown to be strange nearby trajectories separate exponentially on the average moreover the poincare sections exhibit the stretching and folding that is characteristic of strange attractors

the necessity for a time local dimension in systems with time varying attractors abstract we show that a simple non linear system for ordinary differential equations may possess a time varying attractor dimension this indicates that it is infeasible to characterize eeg and meg time series with a single time global dimension we suggest another measure for the description of non stationary attractors

two boundary value problems for the ginzburg landau equation abstract two boundary value problems for the ginzburg landau equation are considered extensive numerical calculations have been performed in each case including bifurcation histories spectral analysis poincare sections and hausdorff dimension estimates the approach to the inviscid limit is given detailed treatment in this case universal behavior has been found to exist arguments are presented to account for this behavior

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

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

estimations of domains with cycles abstract a method for estimating domains with limit cycles and finding surfaces with the traces of all cycles is proposed corresponding estimations of domains with cycles for lorenz and rossler systems are indicated