chaos control in economical model by time delayed feedback method abstract a two dimensional map describing chaotic behaviour of an economic model has been stabilized on various periodic orbits by the use of pyragas time delayed feedback control the method avoids fancy data processing used in the ott grebogi yorke approach and is based solely on the plain measurement and time lag of a scalar signal which in our case is a value of sales of a firm following an active investment strategy behrens feichtinger model we show that the application of this control method is very straightforward and one can easily switch from a chaotic trajectory to a regular periodic orbit and simultaneously improve the system s economic properties

research on dynamics in a resource extraction game with bounded rationality abstract based on bounded rationality a linear dynamic system is proposed in this work for the duopoly game of renewable resource extraction this dynamics reflects the decision makers dynamical output strategy consisting of all the nash equilibriums in every two adjacent periods the resource growth rate the discount rate and the expected extraction rate are the major parameters in this system the system stability and the equilibrium characteristics of the stable state are analyzed numerical simulations are made to show the influence of all the parameters on the speed for the system to approaches its stable equilibrium by the mathematical analysis we find that if the discount is smaller or the expected extraction rate is larger the system will converge in shorter time and approach a stable state with lager resource reserve and with larger resource output so we draw the conclusion that decision makers focusing on the long term profits is helpful to sustainable development on natural resource market in the long run

proof of the symmetry of the off diagonal hadamard seeley dewitt s coefficients in c lorentzian manifolds by a local wick rotation completing the results achieved in a previous paper we prove the symmetry of hadamard seeley dewitt off diagonal coefficients in smooth d dimensional lorentzian manifolds this result is relevant because it plays a central role in physics in particular in the theory of the stress energy tensor renormalization procedure in quantum field theory in curved spacetime to this end it is shown that in any lorentzian manifold a sort of local wick rotation of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinate are appropriate no time like killing field is necessary such a local wick rotation analytically continues the lorentzian metric in a neighborhood of any point more generally in a neighborhood of a space like cauchy hypersurface into a riemannian metric the continuation locally preserves geodesically convex neighborhoods in order to make rigorous the procedure the concept of a complex pseudo riemannian not hermitian or kahlerian manifold is introduced and some features are analyzed using these tools the symmetry of hadamard seeley dewitt off diagonal coefficients is proven in lorentzian analytical manifolds by analytical continuation of the symmetric riemannian heat kernel coefficients this continuation is performed in geodesically convex neighborhoods in common with both the metrics then the symmetry is generalized to c non analytic lorentzian manifolds by approximating lorentzian c metrics by analytic metrics in common geodesically convex neighborhoods

analytical investigation of modulated time delayed feedback control the influence of time dependent control parameters on time delayed feedback schemes for control of chaos is investigated by analytical means for the logistic map the linear stability of the period two orbit subjected to a modulated time delayed feedback loop is calculated we find enhanced control performance due to phase lags between the periodic orbit and the controller

analytical properties and optimization of time delayed feedback control time delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems if the equations governing the system dynamics are known the success of the method can be predicted by a linear stability analysis of the desired orbit unfortunately the usual procedures for evaluating the floquet exponents of such systems are rather intricate we show that the main stability properties of the system controlled by time delayed feedback can be simply derived from a leading floquet exponent defining the system behavior under proportional feedback control optimal parameters of the delayed feedback controller can be evaluated without an explicit integration of delay differential equations the method is valid for low dimensional systems whose unstable periodic orbits are originated from a period doubling bifurcation and is demonstrated for the rossler system and the duffing oscillator

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

homogeneous nucleation of a solid solid dilatational phase transformation abstract the problem of homogeneous coherent nucleation of a spherical particle in an infinite matrix is considered a landau ginzburg type potential is used to describe the material response the underlying landau potential is taken to be of the 2 3 4 type and the gradient energy contribution is taken to be quadratic the nucleation problem is posed as an energy extremum problem and the finite element method in conjunction with a perturbed lagrangian algorithm is used to obtain solutions with nucleus structure the present nonlinear model spans the range from classical to nonclassical nucleation and exhibits many of the physical phenomena associated with nonclassical nucleation including divergence in radius and interface thickness of the critical nucleus and vanishing of the nucleation energy as the instability temperature is approached

on the stress energy tensor of quantum fields in curved spacetimes comparison of different regularization schemes and symmetry of the hadamard seeley dewitt coefficients we review a few rigorous and partly unpublished results on the regularisation of the stress energy in quantum field theory on curved spacetimes 1 the symmetry of the hadamard seeley dewitt coefficients in smooth riemannian a lorentzian spacetimes 2 the equivalence of the local function and the hadamard point splitting procedure in smooth static spacetimes 3 the equivalence of the dewitt schwinger and the hadamard point splitting pro cedure in smooth riemannian and lorentzian spacetimes

non linear dynamics in adaptive control chaotic and periodic stabilization abstract in this paper the non linear features of adaptive control algorithms are highlighted using a simple linear discrete time example based on classical design it is demonstrated that in the presence of undermodelling errors non linear phenomena in the feedback gain such as limit cycles and even chaos arise despite these complicated dynamics robust stabilization of the plant can still occur for the class of undermodelling errors considered the set of plants stabilizable by this adaptive controller is completely characterized

influence of stable floquet exponents on time delayed feedback control the performance of time delayed feedback control is studied by linear stability analysis analytical approximations for the resulting eigenvalue spectrum are proposed our investigations demonstrate that eigenbranches that develop from the stable lyapunov exponents of the free system also have a strong influence on the control properties either by hybridization or by a crossing of branches which interchanges the role of the leading eigenvalue our findings are confirmed by numerical analysis of two particular examples the toda and the r ossler models more important is the verification by actual electronic circuit experiments here the observed reduction of control domains can be attributed to these additional eigenvalue branches the investigations lead to a thorough analytical understanding of the stability properties in time delayed feedback systems

complex dynamics analysis for a duopoly stackelberg game model with bounded rationality in view of the effect of differences between plan products and actual products a duopoly stackelberg model of competition on output is formulated the firms announce plan products sequentially in planning phase and act simultaneously in production phase backward induction is used to solve subgame nash equilibrium the equilibrium outputs and equilibrium profits are affected by cost coefficients for the duopoly stackelberg model a nonlinear dynamical system which describes the time evolution with bounded rationality is analyzed the equilibria of the corresponding discrete dynamical systems are investigated the local stability analysis has been carried out the stability of nash equilibrium gives rise to complex dynamics as some parameters of the model are varied numerical simulations were used to show bifurcation diagram stability region and chaos it is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos

local wick polynomials and time ordered products of quantum fields in curved spacetime in order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime it is necessary to construct wick polynomials and their time ordered products for the noninteracting theory a construction of these quantities has recently been given by brunetti fredenhagen and kohler and by brunetti and fredenhagen but they did not impose any locality or covariance condition in their constructions as a consequence their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters in this paper we construct an extended wick polynomial algebra large enough to contain the wick polynomials and their time ordered products by generalizing a construction of dutsch and fredenhagen to curved spacetime we then define the notion of a local covariant quantum field and seek a definition of local wick polynomials and their time ordered products as local covariant quantum fields we introduce a new notion of the scaling behavior of a local covariant quantum field and impose scaling requirements on our local wick polynomials and their time ordered products as well as certain additional requirements such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric for a given polynomial order in powers of the field we prove that these conditions uniquely determine the local wick polynomials and their time ordered products up to a finite number of parameters these parameters correspond to the usual renormalization ambiguities occurring in minkowski spacetime together with additional parameters corresponding to the coupling of the field to curvature we also prove existence of local wick polynomials however the issue of existence of local time ordered products is deferred to a future investigation

tripoly stackelberg game model this paper is devoted to introduce and study a stackelberg game consisting of three competed firms the three firms are classified as a leader which is the first firm and the other two firms are called the followers a linear inverse demand function is used in addition a quadratic cost based on an actual and announced quantities is adopted based on bounded rationality a three dimensional discrete dynamical system is constructed for the system the backward induction is used to solve the system and to get nash equilibrium the obtained results are shown that nash equilibrium is unique and its stability is affected by the systems parameters by which the system behaves chaotically due to bifurcation and chaos appeared some numerical experiments are performed to portrays such chaotic behavior a control scheme is used to return the system back to its stability state and is supported by some simulations

bifurcation in model reference adaptive control systems abstract we study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism exact stability boundaries are computed and different routes to chaotic behavior and global instability are described typically we observed a region of period doubling and hopf bifurcations similar to those observed in the ziegler nichols approach to pid control design the analysis applies to higher order and certain nonlinear systems as well

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

a new method to control chaos in an economic system in this paper the method to control chaos by using phase space compression is applied to economic systems because of economic significance of state variable in economic dynamical systems the values of state variables are positive due to capacity constraints and financial constraints we can control chaos by adding upper bound or lower bound to state variables in economic dynamical systems which is different from the chaos stabilization in engineering or physics systems the knowledge about system dynamics and the exact variety of parameters are not needed in the application of this control method so it is very convenient to apply this method two kinds of chaos in the dynamic duopoly output systems are stabilized in a neighborhood of an unstable fixed point by using the chaos controlling method the results show that performance of the system is improved by controlling chaos in practice owing to capacity constraints financial constraints and cautious responses to uncertainty in the world the firm often restrains the output advertisement expenses research cost etc to confine the range of these variables fluctuation this shows that the decision maker uses this method unconsciously in practice

persistence of chaos in a time delayed feedback controlled duffing system this paper concerns global phase structures of a time delayed feedback controlled two well duffing system the remains of a global stretch and fold structure along an unstable manifold which develops from an unstable fixed point in function space reveals that the global chaotic dynamics is inherited from the original system by the controlled system the remains of the original chaotic dynamics causes a highly complicated domain of attraction for target orbits and a long chaotic transient before convergence

delayed feedback control via minimum entropy strategy in an economic model abstract in this paper minimum entropy me algorithm for controlling chaos is applied to the behrens feichtinger model as a discrete time dynamic system which models a drug market the me control is implemented through delayed feedback it is assumed that the dynamic equations of the system are not known so the proper feedback gain cannot be obtained analytically from the system equations in the me approach the feedback gain is obtained and adapted in such a way that the entropy of the system converges to zero hence a fixed point of the system will be stabilized application of the proposed method with different economic control strategies is numerically investigated simulation results show the effectiveness of the me method to control chaos in economic systems with unknown dynamic equations

conformal generally covariant quantum field theory the scalar field and its wick products in this paper we generalize the construction of generally covariant quantum theories given in bfv03 to encompass the conformal covariant case after introducing the abstract framework we discuss the massless conformally coupled klein gordon field theory showing that its quantization corresponds to a functor between two certain categories at the abstract level the ordinary fields could be thought of as natural transformations in the sense of category theory we show that the wick monomials without derivatives wick powers can be interpreted as fields in this generalized sense provided a non trivial choice of the renormalization constants is given a careful analysis shows that the transformation law of wick powers is characterized by a weight and it turns out that the sum of fields with different weights breaks the conformal covariance at this point there is a difference between the previously given picture due to the presence of a bigger group of covariance it is furthermore shown that the construction does not depend upon the scale appearing in the hadamard parametrix used to regularize the fields finally we briefly discuss some further examples of more involved fields

diophantine approximation and badly approximable sets let x d be a metric space and d a compact subspace of x which supports a non atomic finite measure m we consider natural classes of badly approximable subsets of loosely speaking these consist of points in which stay clear of some given set of points in x the classical set bad of badly approximable numbers in the theory of diophantine approximation falls within our framework as do the sets bad i j of simultaneously badly approximable numbers under various natural conditions we prove that the badly approximable subsets of have full hausdorff dimension applications of our general framework include those from number theory classical complex p adic and formal power series and dynamical systems iterated function schemes rational maps and kleinian groups

a self adjusted monte carlo simulation as a model for financial markets with central regulation abstract properties of the self adjusted monte carlo algorithm applied to 2d ising ferromagnet are studied numerically the endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random walk of the temperature that converges to criticality without an external tuning the robustness of a stationary regime with respect to partial accessibility of the information is demonstrated several statistical and scaling aspects have been identified which allow to establish an alternative spin lattice model of the financial market it turns out that our model alike model suggested by bornholdt int j mod phys c 12 2001 667 may be described by levy type stationary distribution of feedback variations with unique exponent 1 3 3 however the differences reflected by hurst exponents suggest that resemblances between the studied models seem to be non trivial

drift instabilities and chaos in forecasting and adaptive decision theory abstract bifurcation theory shows that policy adaptation and the rational expectations hypothesis of macro economics can be used to explain unpredictability rapid changes in solution structure and chaos in decision problems with uncertainty structural errors lead to catastrophic instability and forecasts become irrelevant short evaluation horizon and the application of measures designed to give quick response give multiperiodicity and chaos finally wrong interpretations of the context lead to global bifurcations laminar drift complacency and chaotic bursting the discrete map representing these dynamics is of interest in its own right it is non invertible and displays bifurcation behaviour not commonly seen in systems derived from physical considerations

small amplitude chaos and ergodicity in adaptive control abstract the theory for continuous iterated maps on the real line is used to study the dynamics of a continuous family of one parameter adaptive systems we establish sufficient and necessary conditions for uniform asymptotic stability and ultimate boundedness exact bifurcation boundaries and sufficient conditions for the existence of chaotic attractors and ergodicity of the estimated parameter it is argued that the chaotic dynamics are structurally stable that they persist in higher dimensional adaptive control systems and that they do not necessarily lead to poor performance when the controller is modified to deal with the infinite drift and small divisor problems a novel modification involving a sign change in the adaptive law is proposed

analysis of nonlinear triopoly game with heterogeneous players a nonlinear triopoly game with heterogeneous players is presented we consider three types of players boundedly rational adaptive and naive a triopoly game is modelled by a three dimensional discrete dynamical system the stability conditions of the equilibrium points are analyzed numerical simulations are used to show bifurcation diagrams phase portraits sensitive dependence on initial conditions and fractal dimension the chaotic behavior of the model has been stabilized on the nash equilibrium point by the use of the pyragas delay feedback control method

sustaining stable dynamics of a fractional order chaotic financial system by parameter switching in this paper a simple parameter switching ps methodology is proposed for sustaining the stable dynamics of a fractional order chaotic financial system this is achieved by switching a controllable parameter of the system within a chosen set of values and for relatively short periods of time the effectiveness of the method is confirmed from a computer aided approach and its applications to chaos control and anti control are demonstrated in order to obtain a numerical solution of the fractional order financial system a variant of the grunwald letnikov scheme is used extensive simulation results show that the resulting chaotic attractor well represents a numerical approximation of the underlying chaotic attractor which is obtained by applying the average of the switched values moreover it is illustrated that this approach is also applicable to the integer order financial system

comparison of time delayed feedback schemes for spatiotemporal control of chaos in a reaction diffusion system with global coupling time delayed feedback control for stabilizing time periodic spatial patterns is investigated in a generic reaction diffusion system with global coupling we focus on the case of low dimensional chaos where unstable patterns admit only a single unstable mode spatial degrees of freedom are taken into account to define different control schemes the efficiency of these schemes is discussed where control forces are motivated by physical requirements as well as by the possibility of obtaining analytically exact results we find that control schemes that contain the full feedback of the inhibitor variable may finally destroy the control performance thus schemes that omit the inhibitor might be more efficient our numerical findings are explained in terms of floquet spectra and compared with analytical solutions of particular coupling schemes

global wave parametrices on globally hyperbolic spacetimes abstract in a recent work the first named author levitin and vassiliev have constructed the wave propagator on a closed riemannian manifold m as a single oscillatory integral global both in space and in time with a distinguished complex valued phase function in this paper first we give a natural reinterpretation of the underlying algorithmic construction in the language of ultrastatic lorentzian manifolds subsequently we show that the construction carries over to the case of static backgrounds thanks to a suitable reduction to the ultrastatic scenario finally we prove that the overall procedure can be generalised to any globally hyperbolic spacetime with compact cauchy surfaces as an application we discuss how from our procedure one can recover the local hadamard expansion which plays a key role in all applications in quantum field theory on curved backgrounds

almost no points on a cantor set are very well approximable we prove that almost no numbers in cantor9s middle thirds set are very well approximable by rationals more generally we discuss diophantine properties of almost every point where almost every is understood relative to any measure on the real line satisfying a decay condition introduced in the work of veech

a note on badly approximabe sets in projective space recently ghosh and haynes j reine angew math 712 39 50 2016 proved a khintchine type result for the problem of diophantine approximation in certain projective spaces in this note we complement their result by observing that a jarnik type result also holds for badly approximable points in real projective space in particular we prove that the natural analogue in projective space of the classical set of badly approximable numbers has full hausdorff dimension when intersected with certain compact subsets of real projective space furthermore we also establish an analogue of khintchine s theorem for convergence relating to intrinsic approximation of points in these compact sets

on the distribution of points in projective space of bounded height in this paper we consider the uniform distribution of points in compact metric spaces we assume that there exists a probability measure on the borel subsets of the space which is invariant under a suitable group of isometries in this setting we prove the analogue of weyl s criterion and the erdos tur an inequality by using orthogonal polynomials associated with the space and the measure in particular we discuss the special case of pro jective space over completions of number elds in some detail an invariant measure in these projective spaces is introduced and the explicit formulas for the orthogonal polynomials in this case are given finally using the analo gous erdos tur an inequality we prove that the set of all projective points over the number eld with bounded arakelov height is uniformly distributed with respect to the invariant measure as the bound increases