variable delay feedback control of unstable steady states in retarded time delayed systems we study the stability of unstable steady states in scalar retarded time delayed systems subjected to a variable delay feedback control the important aspect of such a control problem is that time delayed systems are already infinite dimensional before the delayed feedback control is turned on when the frequency of the modulation is large compared to the system s dynamics the analytic approach consists of relating the stability properties of the resulting variable delay system with those of an analogous distributed delay system otherwise the stability domains are obtained by a numerical integration of the linearized variable delay system the analysis shows that the control domains are significantly larger than those in the usual time delayed feedback control and that the complexity of the domain structure depends on the form and the frequency of the delay modulation

faces of the cone of euclidean distance matrices characterizations structure and induced geometry in this paper we obtain new characterizations of the faces of the cone of euclidean distance matrices in one case the characterization is based on a special subspace associated with each distance matrix in other case on linear restrictions of coordinate matrices we also relate the faces to the supporting hyperplanes of the cone and we show how the supporting hyperplanes induce certain geometry on the configurations that belong to that face

on stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls abstract the paper discusses stabilizing effects of some time delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations first we derive explicit delay dependent stability conditions that are applicable to a family of time delayed systems with simultaneously triangularizable system matrices then using this criterion and other argumentation we employ diagonal delayed feedback controls of conventional and pyragas type to stabilize unstable steady states of the studied autonomous system more precisely we formulate explicit non improvable and immediately applicable conditions on time delay and feedback strength that enable such a stabilization as an illustration we stabilize the unstable steady states of the rossler dynamical system considered under the standard choice of entry parameters when the uncontrolled system displays a chaotic behavior also we consider a non diagonal feedback control whose rotational gain matrix involving a feedback strength and phase commutes with the jacobi matrix of the uncontrolled system and show its larger stabilization potential with respect to the appropriate diagonal control the obtained results are tested by numerical experiments and confronted with the existing results as a supplement we provide matlab codes supporting theoretical conclusions

control of unstable steady states by extended time delayed feedback time delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states we present an application of extended time delay autosynchronization introduced by socolar et al phys rev e 50 3245 1994 to an unstable focus this system represents a generic model of an unstable steady state which can be found for instance in hopf bifurcation in addition to the original controller design we investigate effects of control loop latency and a bandpass filter on the domain of control furthermore we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase we present an analysis of the domain of control and support our results by numerical calculations

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

moore penrose inverse of a euclidean distance matrix abstract we obtain expressions for the moore penrose inverse of a euclidean distance matrix edm that are determined only by the positive semidefinite matrix associated with the edm the results complement formulas for the moore penrose inverse of an edm given in balaji and bapat 2007 2 a formula for the inverse of a principal submatrix of an edm is also derived whose expression uses the schur complement of the laplacian of the edm as an application we obtain an expression for the terminal wiener index of a tree

taking advantage of symmetries gathering of many asynchronous oblivious robots on a ring one of the recently considered models of robot based computing makes use of identical memoryless mobile units placed in nodes of an anonymous graph the robots operate in look compute move cycles in one cycle a robot takes a snapshot of the current configuration look takes a decision whether to stay idle or to move to one of the nodes adjacent to its current position compute and in the latter case makes an instantaneous move to this neighbor move cycles are performed asynchronously for each robot in such a restricted scenario we study the influence of symmetries of the robot configuration on the feasibility of certain computational tasks more precisely we deal with the problem of gathering all robots at one node of the graph and propose a solution based on a symmetry preserving strategy when the considered graph is an undirected ring and the number of robots is sufficiently large more than 18 such an approach is proved to solve the problem for all starting situations as long as gathering is feasible in this way we also close the open problem of characterizing symmetric situations on the ring which admit a gathering r klasing e markou a pelc gathering asynchronous oblivious mobile robots in a ring theoret comput sci 390 1 2008 27 39 the proposed symmetry preserving approach which is complementary to symmetry breaking techniques found in related work appears to be new and may have further applications in robot based computing

on certain linear mappings between inner product and squared distance matrices abstract we obtain the spectral decomposition of four linear mappings the first is a mapping of the linear hull of all centered inner product matrices onto the linear hull of all the induced squared distance matrices it is based on the natural generalization of the cosine law of elementary euclidean geometry the other three mappings studied are 1 the adjoint and 1 extensions and applications particularly to multidimensional scaling are discussed in some detail

on unit spherical euclidean distance matrices which differ in one entry abstract a unit spherical euclidean distance matrix edm d is a matrix whose entries can be realized as the interpoint squared euclidean distances of n points on a unit sphere in this paper given such a d and 1 k l n we present a characterization of the set of all unit spherical edms whose entries agree with those of d except possibly with the entry in the klth and lkth positions as a result we show that this set can be discrete consisting of one or two elements or it can be continuous the results are derived using two alternative approaches the second of which is based on cayley menger matrices

two theorems on euclidean distance matrices and gale transform abstract we present a characterization of those euclidean distance matrices edms d which can be expressed as d e c for some nonnegative scalar and some correlation matrix c where e is the matrix of all ones this shows that the cones cone e e n cone e e n d n where e n is the elliptope set of correlation matrices and d n is the closed convex cone of edms the characterization is given using the gale transform of the points generating d we also show that given points p 1 p 2 p n r r for any scalars 1 2 n such that j 1 n j p j 0 j 1 n j 0 we have j 1 n j p i p j 2 for all i 1 n for some scalar independent of i

analysis and comparison of multiple delay schemes for controlling unstable fixed points of discrete maps we investigate theoretically the stabilization of a fixed point of a discrete one dimensional nonlinear map by applying small perturbations to an accessible system parameter or variable the size of the perturbations is determined in real time using feedback schemes incorporating only the dynamical state of the system and its state at previous iterates without making a comparison to a reference state in particular we compare and contrast two algorithms extended time delay autosynchronization which uses an infinite series of past iterates with weights that decay by a factor of r with each time step and n time delay autosynchronization which uses an average of n past iterates with equal weights the range of feedback parameters that successfully stabilize the fixed point and the robustness of the schemes to noise are determined it is found that the domain of control for the two schemes is similar for appropriately matched values of r and n and that n time delay autosynchronization tends to be less sensitive to noise s1063 651x 98 02706 8

a remark on the faces of the cone of euclidean distance matrices a new characterization of the faces of the cone of euclidean distance matrices edms was recently obtained by tarazaga in terms of lgs d a special subspace associated with each edm d in this note we show that lgs d is nothing but the gale subspace associated with edms

block matrices and multispherical structure of distance matrices abstract the block structure of a matrix and its relation to the block structure of the corresponding eigenvectors is investigated a set of points is said to have multispherical structure if they lie on a collection of concentric spheres when the centroid of each of the clusters lies at the common center the associated distance matrix has a block structure with simple relations between the blocks further such block structure may be recognized from the structure of the eigenvectors of the distance matrix a computational procedure is proposed to find the least number of concentric spheres containing the points represented by a distance matrix

periodic patterns in a ring of delay coupled oscillators we describe the appearance and stability of spatiotemporal periodic patterns rotating waves in unidirectional rings of coupled oscillators with delayed couplings we show how delays in the coupling lead to the splitting of each rotating wave into several new ones the appearance of rotating waves is mediated by the hopf bifurcations of the symmetric equilibrium we also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain the phenomena are shown for the stuart landau oscillators as well as for the coupled fitzhugh nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses

majorization for the eigenvalues of euclidean distance matrices abstract this paper investigates the relation between the eigenvalues of a euclidean distance matrix edm and those of the corresponding positive semidefinite matrix more precisely let d 1 and d 2 be two edms and let b 1 and b 2 be the corresponding positive semidefinite matrices such that d i b i i 1 2 in this paper when the eigenvalues of b 1 majorizes those of b 2 a condition under which the eigenvalues of d 1 majorizes those of d 2 is derived

connections between the real positive semidefinite and distance matrix completion problems abstract though the real symmetric positive semidefinite psd matrices and the euclidean distance matrices are closely related exact relationships between the corresponding completion problems are not apparent we establish strong partial relationships of two types this permits the transfer of some insights from one problem to the other and allows computational tools for the psd problem to be used for the distance problem

conversion of stability in systems close to a hopf bifurcation by time delayed coupling we propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a hopf bifurcation we consider two delay coupled normal forms for hopf bifurcation and demonstrate the conversion of stability i e an interchange between the sub and supercritical hopf bifurcation the control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking the main method and the results are applicable to a wide class of systems showing hopf bifurcations for example the van der pol oscillator the analytical theory is supported by numerical simulations of two delay coupled van der pol oscillators which show good agreement with the theory

estimating the gap of finite metric spaces of strict p negative type abstract let x d be a finite metric space this paper first discusses the spectrum of the p distance matrix of a finite metric space of p negative type and then gives upper and lower bounds for the so called gap x p of a finite metric space of strict p negative type furthermore estimations for x p under a certain gluing construction for finite metric spaces are given and finally be applied to finite ultrametric spaces

hadamard inverses square roots and products of almost semidefinite matrices abstract let a aij be an n n symmetric matrix with all positive entries and just one positive eigenvalue bapat proved then that the hadamard inverse of a given by a 1 1 a ij is positive semidefinite we show that if moreover a is invertible then a 1 is positive definite we use this result to obtain a simple proof that with the same hypotheses on a except that all the diagonal entries of a are zero the hadamard square root of a given by a 1 2 a ij 1 2 has just one positive eigenvalue and is invertible finally we show that if a is any positive semidefinite matrix and b is almost positive definite and invertible then a b 1 e t b 1 e a

on euclidean distance matrices abstract if a is a real symmetric matrix and p is an orthogonal projection onto a hyperplane then we derive a formula for the moore penrose inverse of pap as an application we obtain a formula for the moore penrose inverse of an euclidean distance matrix edm which generalizes formulae for the inverse of a edm in the literature to an invertible spherical edm we associate a laplacian matrix which we define as a positive semidefinite n n matrix of rank n 1 and with zero row sums and prove some properties known results for distance matrices of trees are derived as special cases in particular we obtain a formula due to graham and lovasz for the inverse of the distance matrix of a tree it is shown that if d is a nonsingular edm and l is the associated laplacian then d 1 l is nonsingular and has a nonnegative inverse finally infinitely divisible matrices are constructed using edms

simple expressions for the long walk distance abstract the walk distances in graphs are defined as the result of appropriate transformations of the k 0 ta k proximity measures where a is the weighted adjacency matrix of a connected weighted graph and t is a sufficiently small positive parameter the walk distances are graph geodetic moreover they converge to the shortest path distance and to the so called long walk distance as the parameter t approaches its limiting values in this paper simple expressions for the long walk distance are obtained they involve the generalized inverse minors and inverses of submatrices of the symmetric irreducible singular m matrix l i a where is the perron root of a

a geometrical characterization of strongly regular graphs abstract we give a necessary and sufficient condition of a euclidean representation of a simple graph to be spherical moreover we show a characterization of strongly regular graphs from the view point of euclidean representations of a graph from this characterization we define a natural generalized concept of a strongly regular graph closely related to euclidean designs and codes

pbc based pulse stabilization of periodic orbits abstract we investigate prediction based schemes to stabilize periodic solutions to potentially chaotic systems of periodic difference equations using pulses at times being a multiple of the period by introducing the concept of a stability domain we obtain precise information on the possibility to stabilize given solutions to avoid destabilizing bifurcations as well as on the magnitude of the required control

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

on group inverses of m matrices with uniform diagonal entries abstract in two recent works the condition of the diagonal entries of the group inverse of a singular and irreducible m matrix being uniform constant has arisen in resistive electrical circuits and in the effect upon the perron root of certain diagonal perturbation of a nonnegative matrix in this paper we first show a negative result that the group inverse of the laplacian matrix of an undirected weighted graph g on n vertices with a cutpoint cannot have uniform diagonal this includes the case when g is a tree we characterize however all weighted n cycles g whose laplacian has a group inverse with a uniform diagonal finally we consider the mean first passage matrix m of an ergodic markov chain with a doubly stochastic transition matrix t we show that if the group inverse of i t has a uniform diagonal then the group inverse of the m matrix m i m is again an m matrix

gathering of robots on anonymous grids and trees without multiplicity detection the paper studies the gathering problem on grid and tree networks a team of robots placed at different nodes of the input graph has to meet at some node and remain there robots operate in look compute move cycles in one cycle a robot perceives the current configuration in terms of occupied nodes look decides whether to move toward one of its neighbors compute and in the positive case makes the computed move instantaneously move cycles are performed asynchronously for each robot the problem has been deeply studied for the case of ring networks however the known techniques used on rings cannot be directly extended to grids and trees moreover on rings another assumption concerning the so called multiplicity detection capability was required in order to accomplish the gathering task that is a robot is able to detect during its look operation whether a node is empty or occupied by one robot or occupied by an undefined number of robots greater than one in this paper we provide a full characterization about gatherable configurations for grids and trees in particular we show that on these topologies the multiplicity detection is not required very interestingly sometimes the problem appears trivial as it is for the case of grids with both odd sides while sometimes the involved techniques require new insights with respect to the well studied ring case moreover our results reveal the importance of structures like grids and trees that allow to overcome the multiplicity detection with respect to the ring case

circum euclidean distance matrices and faces abstract we study the structure of circum euclidean distance matrices those euclidean distance matrices generated by points lying on a hypersphere we show for example that such euclidean distance matrices are characterized as having constant row sums and they constitute the interior of the cone of all euclidean distance matrices also we provide a formula for computing the radius of a representing configuration in the smallest embedding dimension r and show that rk d r 1 finally we obtain a geometric characterization of the faces of this cone given a configuration of points and its euclidean distance matrix d any matrix in the minimal face containing d comes from a configuration that is a linear perturbation of the points that generate d

gathering of oblivious robots on infinite grids with minimum traveled distance abstract a largely studied version of the gathering problem asks to move a set of robots initially placed at different vertices of an anonymous graph toward a common vertex and to let them remain at such a vertex asynchronous robots move based on the so called look compute move model each time a robot wakes up it perceives the current configuration in terms of occupied vertices look it decides whether to move toward one of its neighbors compute and then it performs the computed move move eventually so far the main goal has been to detect the minimal assumptions that allow to accomplish the task without taking care of any cost measure in this paper we are interested in optimal algorithms in terms of total number of moves we consider infinite grids and we fully characterize when optimal gathering is achievable by providing a distributed algorithm

distance matrices and regular figures abstract a regular figure which includes all regular polygons is a set of points on a hypersphere whose center coincides with their centroid we characterize all regular figures as those whose points generate a euclidean distance matrix edm with eigenvector e the vector of all ones restricting the classical maps of schoenberg gower and critchley for all edms to the subcone of edms with eigenvector e yields new geometrical information about the generating points and a simple formula for the radius of the hypersphere

controlling coherence of noisy and chaotic oscillators by a linear feedback abstract we analyze the dynamics of a noisy limit cycle oscillator coupled to a general passive linear system we analytically demonstrate that the phase diffusion constant which characterizes the coherence of the oscillations can be efficiently controlled theoretical analysis is performed in the framework of linear and gaussian approximations and is supported by numerical simulations we also demonstrate numerically the coherence control of a chaotic system

no chattering sliding mode control chaos in hindmarsh rose neurons with uncertain parameters a hindmarsh rose hr model was constructed from voltage clamp data to provide a simple description of the patterned activity seen in molluscan neurons its complex dynamics characters are presented including the phase trajectory the lyapunov exponents and the poincare map furthermore a no chattering sliding mode control method for the hindmarsh rose hr model with uncertain parameters and bounded external disturbances is proposed and it can control the system to any point and any periodic orbit both the theoretical analysis and the simulation results are presented to confirm the validity of the control method

delay and periodicity systems with time delay play an important role in modeling of many physical and biological processes in this paper we describe generic properties of systems with time delay which are related to the appearance and stability of periodic solutions in particular we show that delay systems generically have families of periodic solutions which are reappearing for infinitely many delay times as delay increases the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions we also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers we show that the spectrum of multipliers can be split into two parts pseudocontinuous and strongly unstable the pseudocontinuous part of the spectrum mediates destabilization of periodic solutions

inequalities and equalities associated with the campbell youla generalized inverse of the indefinite admittance matrix of resistive networks abstract matrix theoretic interpretations are obtained for the campbell youla inverse and its associated terminal weight numbers and network diameter these concepts are useful for the effective modeling of resistive electrical networks in our companion paper we explore some related graph theory geometric interpretations were recently given by fiedler

the rendezvous search problem the author considers the problem faced by two people who are placed randomly in a known search region and move about at unit speed to find each other in the least expected time this time is called the rendezvous value of the region it is shown how symmetries in the search region may hinder the process by preventing coordination based on concepts such as north or clockwise a general formulation of the rendezvous search problem is given for a compact metric space endowed with a group of isometrics which represents the spatial uncertainties of the players these concepts are illustrated by considering upper bounds for various rendezvous values for the circle and an arbitrary metric network the discrete rendezvous problem on a cycle graph for players restricted to symmetric markovian strategies is then solved finally the author considers the problem faced by two people on an infinite line who each know the distribution of the distance but not the direction to each other

influence of control loop latency on time delayed feedback control as realized recently the success of delayed feedback control methods may be significantly restricted by control loop latency i e by an additional delay which acts on the control force we show within a linear stability analysis that such a limitation is caused by the shift of frequency splitting points our analytical results are in good quantitative agreement with numerical exact calculations of the toda oscillator and with data from an electronic circuit experiment

delayed feedback control of chaos bifurcation analysis we study the effect of time delayed feedback control in the form proposed by pyragas on deterministic chaos in the rossler system we reveal the general bifurcation diagram in the parameter plane of time delay and feedback strength k which allows one to explain the phenomena that have been discovered in some previous works we show that the bifurcation diagram has essentially a multi leaf structure that constitutes multistability the larger the time delay the larger the number of attractors that can coexist in the phase space feedback induces a large variety of regimes non existent in the original system among them tori and chaotic attractors born from them finally we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system

on properties of cell matrices in this paper properties of cell matrices are studied a determinant of such a matrix is given in a closed form in the proof a general method for determining a determinant of a symbolic matrix with polynomial entries based on multivariate polynomial lagrange interpolation is outlined it is shown that a cell matrix of size n 1 has exactly one positive eigenvalue using this result it is proven that cell matrices are circum euclidean distance matrices c edm and their generalization k cell matrices are cedm under certain natural restrictions a characterization of k cell matrices is outlined

control of unstable steady states by time delayed feedback methods we show that time delayed feedback methods which have successfully been used to control unstable periodic orbits provide a tool to stabilize unstable steady states we present an analytical investigation of the feedback scheme using the lambert function and discuss effects of both a low pass filter included in the control loop and nonzero latency times associated with the generation and injection of the feedback signal

on yielding and jointly yielding entries of euclidean distance matrices abstract an n n matrix d is a euclidean distance matrix edm if there exist points p 1 p n in some euclidean space such that d i j p i p j 2 for all i j 1 n let d be an edm and let e i j be the n n symmetric matrix with 1 s in the ij th and ji th entries and 0 s elsewhere we say that l i j u i j is the yielding interval of entry d i j if it holds that d t e i j is an edm if and only if l i j t u i j if the yielding interval of entry d i j has length 0 i e if l i j u i j 0 then d i j is said to be unyielding otherwise if l i j u i j then d i j is said to be yielding let d i j and d i k be two unyielding entries of d we say that d i j and d i k are jointly yielding if d t 1 e i j t 2 e i k is an edm for some nonzero scalars t 1 and t 2 in this paper we characterize the yielding and the jointly yielding entries of an edm d in terms of gale transforms of p 1 p n moreover for each yielding entry we present explicit formulae of its yielding interval finally we specialize our results to the case where points p 1 p n are in general position

euclidean graph distance matrices of generalizations of the star graph abstract in this paper a relation between graph distance matrices of the star graph and its generalizations and euclidean distance matrices is considered it is proven that distance matrices of certain families of graphs are circum euclidean their spectrum and generating points are given in a closed form

control of pattern formation by time delay feedback with global and local contributions we consider the suppression of spatiotemporal chaos in the complex ginzburglandau equation by a combined global and local time delay feedback feedback terms are implemented as a control scheme i e they are proportional to the difference between the time delayed state of the system and its current state we perform a linear stability analysis of uniform oscillations with respect to space dependent perturbations and compare with numerical simulations similarly for the fixed point solution that corresponds to amplitude death in the spatially extended system a linear stability analysis with respect to space dependent perturbations is performed and complemented by numerical simulations

feedback control of flow alignment in sheared liquid crystals based on a continuum theory we investigate the manipulation of the nonequilibrium behavior of a sheared liquid crystal via closed loop feedback control our goal is to stabilize a specific dynamical state that is the stationary flow alignment under conditions where the uncontrolled system displays oscillatory director dynamics with in plane symmetry to this end we employ time delayed feedback control tdfc where the equation of motion for the i th component q i t of the order parameter tensor is supplemented by a control term involving the difference q i t ensuremath q i t ensuremath ensuremath tau in this diagonal scheme ensuremath tau is the delay time we demonstrate that the tdfc method successfully stabilizes flow alignment for suitable values of the control strength k and ensuremath tau these values are determined by solving an exact eigenvalue equation moreover our results show that only small values of k are needed when the system is sheared from an isotropic equilibrium state contrary to the case where the equilibrium state is nematic

systematic experimental exploration of bifurcations with noninvasive control we present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment in particular we show how the odd number limitation inherent in popular noninvasive control schemes such as pyragas time delayed or washout filtered feedback control can be overcome for tracking equilibria or forced periodic orbits in experiments to demonstrate the use of our noninvasive control we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability around two saddle node bifurcations folds and a cusp bifurcation

stabilization of a steady state in network oscillators by using diffusive connections with two long time delays the present study shows that diffusive connections with two long time delays can induce the stabilization of a steady state in network oscillators a linear stability analysis shows that if the two delay times retain a proportional relation with a certain bias the stabilization can be achieved independent of the delay times furthermore a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed the procedure has the following two advantages one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology our analytical results are applied to the well known double scroll circuit model on a small world network

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

adaptive control of unknown unstable steady states of dynamical systems a simple adaptive controller based on a low pass filter to stabilize unstable steady states of dynamical systems is considered the controller is reference free it does not require knowledge of the location of the fixed point in the phase space a topological limitation similar to that of the delayed feedback controller is discussed we show that the saddle type steady states cannot be stabilized by using the conventional low pass filter the limitation can be overcome by using an unstable low pass filter the use of the controller is demonstrated for several physical models including the pendulum driven by a constant torque the lorenz system and an electrochemical oscillator linear and nonlinear analyses of the models are performed and the problem of the basins of attraction of the stabilized steady states is discussed the robustness of the controller is demonstrated in experiments and numerical simulations with an electrochemical oscillator the dissolution of nickel in sulfuric acid a comparison of the effect of using direct and indirect variables in the control is made with the use of the controller all unstable phase space objects are successfully reconstructed experimentally

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

technical communique the lambert w function and the spectrum of some multidimensional time delay systems in this note we find an explicit expression for the eigenvalues of a retarded time delay system with one delay for the special case that the system matrices are simultaneously triangularizable which includes the case where they commute using matrix function definitions we define a matrix version of the lambert w function from which we form the expression we prove by counter example that some expressions in other publications on lambert w for time delay systems do not always hold

stabilizing fixed points of time delay systems close to the hopf bifurcation using a dynamic delayed feedback control method this paper deals with the problem of hopf bifurcation control for a class of nonlinear time delay systems a dynamic delayed feedback control method is utilized for stabilizing unstable fixed points near hopf bifurcation using a linear stability analysis we show that under certain conditions of the control parameters and without changing the operating point of the system the onset of hopf bifurcation is delayed meanwhile by applying the center manifold theorem and the normal form theory we obtain formulas for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions of the closed loop system numerical simulations are given to justify the validity of the analytical results for the system controlled by the proposed method

stability domains for time delay feedback control with latency we generalize a known analytical method for determining the stability of periodic orbits controlled by time delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored we discuss the case of extended time delay autosynchronization and show that nontrivial qualitative features of the domain of control observed in experiments can be explained by taking into account the effects of both the unstable eigenmode and a single stable eigenmode in the floquet theory

design and robustness of delayed feedback controllers for discrete systems we study a matrix form of time delay feedback control in the context of discrete time maps of high dimension in almost all cases where standard proportional feedback control methods can achieve control time delay feedback controllers containing only static elements can be designed to achieve identical linear stability properties analysis of an example involving a ring of coupled maps that can be controlled at only two sites demonstrates that the time delay controller equivalent to a standard optimal controller can be equally robust in the presence of noise except at special points in parameter space where the uncontrolled system has a mode with floquet multiplier exactly equal to 1 numerical simulations confirm the results of the analysis

improvement of time delayed feedback control by periodic modulation analytical theory of floquet mode control scheme we investigate time delayed feedback control schemes which are based on the unstable modes of the target state to stabilize unstable periodic orbits the periodic time dependence of these modes introduces an external time scale in the control process phase shifts that develop between these modes and the controlled periodic orbit may lead to a huge increase of the control performance we illustrate such a feature on a nonlinear reaction diffusion system with global coupling and give a detailed investigation for the rossler model in addition we provide the analytical explanation for the observed control features

characterization of symmetric m matrices as resistive inverses abstract we aim here at characterizing those nonnegative matrices whose inverse is an irreducible stieltjes matrix specifically we prove that any irreducible stieltjes matrix is a resistive inverse to do this we consider the network defined by the off diagonal entries of the matrix and we identify the matrix with a positive definite schrodinger operator whose ground state is determined by the lowest eigenvalue of the matrix and the corresponding positive eigenvector we also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric m matrices

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one

time delay induced instabilities in reaction diffusion systems time delay in the kinetic terms of reaction diffusion systems has been investigated it has been shown that short delay beyond a critical threshold may induce spatiotemporal instabilities for unequal diffusivities and appropriate parameter space delay may induce turing instability resulting in stationary patterns and also interesting turing hopf transition with the formation of spirals the theoretical scheme has been numerically explored in two different prototypical reaction diffusion systems