onset of cooperative entrainment in limit cycle oscillators with uniform all to all interactions bifurcation of the order function abstract the concept of order function was previously proposed as the key to a general theory of macroscopic mutual or cooperative entrainment in large populations of limit cycle oscillators with weak interactions such that every element is linked to all the other as well as with weakly dispersed intrinsic frequencies that is limit cycle oscillators that can be modeled by globally coupled phase oscillators with distributed frequencies following previous work a bifurcation theory of the order function is developed on the basis of its self consistent functional equation to elucidate in particular generic scaling behavior of such systems at the onset of cooperative entrainment among other results when the onset is not abrupt the critical exponent of fundamental order parameters turns out to generically differ from the conventional value 1 2 taken by the well studied sinusoidal coupling model as well as by typical mean fields models of thermodynamic phase transitions to which coupled oscillator models investigated here are analogous the theory also reveals what happens in nongeneric cases moreover a criterion is found of whether the bifurcation is normal or inverted all these analytical results and predictions are verified not only by numerically solving the equation of the order function but also by numerical simulations although this paper is mainly concerned with the critical behaviors noncritical regimes are also explored to demonstrate overall power of the order function theory by reproducing simulation results such as average frequency spectra the theory however keeps some room to be further generalized a finding which suggests this is put forth

intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators a theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit cycle oscillators with distributed native frequencies in particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above this peculiar feature is demonstrated by numerical simulations mainly through finite size scaling analyses in the course of exploring its origin we encounter a new concept termed a correlation frequency which provides a natural interpretation of the finite size scaling laws a comment is given on a recent theory by kuramoto and nishikawa to clarify why it contradicts our results

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

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

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

time delay effects on coupled limit cycle oscillators at hopf bifurcation abstract we present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at hopf bifurcation for a simple model consisting of just two oscillators with a time delayed coupling the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death phase locked and incoherent regions a novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators similar results are obtained for an array of n oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified some general analytic results for the n thermodynamic limit are also obtained and the implications of the time delay effects for physical applications are discussed

on approximation problems with zero trace matrices abstract we consider some approximation problems in the linear space of complex matrices with respect to unitarily invariant norms we deal with special cases of approximation of a matrix by zero trace matrices moreover some characterizations of zero trace matrices are given by means of matrix approximation problems

computation of the bit error rate of coherent m ary psk with gray code bit mapping efficient computation of the bit error rate ber for the coherent m ary psk signals with gray code bit mapping is considered a closed form expression for the exact ber of 8 ary psk is presented tight upper and lower bounds on ber are also obtained for m ary psk with larger m

control of unstable steady states by long delay feedback we present an asymptotic analysis of time delayed feedback control of steady states for large delay time by scaling arguments and a detailed comparison with exact solutions we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type insight into the control mechanism is gained by analyzing the eigenvalue spectrum which consists of a pseudocontinuous spectrum and up to two strongly unstable eigenvalues although the standard control scheme generally fails for large delay we find that if the uncontrolled system is sufficiently close to its instability threshold control does work even for relatively large delay times

an approximation for prey predator models with time delay abstract a prototype prey predator p d model in which the effective size of the predator population interacting with its prey follows an instantaneous time delay regarding its total size is considered here a simplified model was derived after substituting the approximation d t d t d t into the above time delay model in order to assess the reliability of the simplified model we performed a comparative study of both models under a wide range of parameter values focusing on the effect of on two issues i the boundary in parameter space between the regions leading either to stable fixed points characteristic of the non delay model both the boundary and the periods and amplitudes obtained for the time delay model can be fairly approximated by the corresponding results for the simplified model

towards easier realization of time delayed feedback control of odd number orbits we develop generalized time delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive floquet exponents which are particularly well suited for experimental realization we construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods in particular it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop finally we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback

delayed feedback control of the lorenz system an analytical treatment at a subcritical hopf bifurcation we develop an analytical approach for the delayed feedback control of the lorenz system close to a subcritical hopf bifurcation the periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by a conventional delayed feedback control technique we utilize a modification based on an unstable delayed feedback controller the analytical approach employs the center manifold theory and the near identity transformation we derive the characteristic equation for the floquet exponents of the controlled orbit in an analytical form and obtain simple expressions for the threshold of stability as well as for an optimal value of the control gain the analytical results are supported by numerical analysis of the original system of nonlinear differential difference equations

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

decision feedback differential detection based on linear prediction for 16dapsk signals transmitted over flat ricean fading channels in this article prediction based decision feedback differential detection df dd for 16 level differentially encoded amplitude phase shift keying is proposed unlike previously reported df dd schemes this scheme provides a performance gain over conventional differential detection under general ricean fading conditions a further important advantage of the novel scheme is that it is able to compensate a small carrier frequency offset the linear predictor coefficients may be updated using the recursive least squares algorithm which can start blind i e without a priori knowledge about the channel statistics and without a training sequence this makes the scheme attractive for application in mobile communications since the statistics of a nonstationary mobile channel can be tracked

reaction cattaneo systems with fluctuating relaxation time a reaction cattaneo equation with fluctuating relaxation time of the diffusive flux has been explored it has been shown that depending on the strength of fluctuations the dynamical system exhibits new oscillatory solutions as a result of hopf and double hopf bifurcations leading to spatiotemporal patterns this analysis has been applied to two model nonlinear systems

amplitude death in complex networks induced by environment we present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system we develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death an important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix our results are fully supported by the detailed numerical analysis for different network topologies

dynamics of a large system of coupled nonlinear oscillators abstract we consider the interaction of a large number of limit cycle oscillators with linear all to all coupling and a distribution of natural frequencies the system exhibits extremely rich dynamics as the coupling strength and the width of the frequency distribution are varied we find a variety of steady behaviors that can be described by a stationary distribution in phase space frequency locking amplitude death incoherence and partial locking an unexpected result is that the system can also exhibit unsteady behavior in which the phase space distribution evolves periodically quasiperiodically or even chaotically the simple form of the model allows us to derive several analytical results the stability boundaries of amplitude death and incoherence are found explicitly rigorous results on the existence and stability of frequency locking are also obtained

trace characterizations and socle identifications in banach algebras abstract as a follow up to a paper of d petz and j zemanek 1 a number of equivalent conditions which characterize the trace among linear functionals on matrix algebras finite rank operators and the socle elements of semisimple banach algebras in general are given moreover the converse problem is also addressed that is given the equivalence of certain conditions which characterize the trace what can be said about the structure of the socle in particular we characterize those socles isomorphic to matrix algebras in this manner as well as those socles which are minimal two sided ideals

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

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

some basic remarks on eigenmode expansions of time delay dynamics abstract we describe in elementary terms how eigenmode expansions can be used to deal with differential difference equations as particular applications we present the full analytical solution of linear stochastic time delay systems and the weakly nonlinear analysis of nonlinear differential difference equations in the limit of large time delay our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the lambert w function and on the explicit formula for the eigenfunctions of the adjoint equation

an inequality for hilbert schmidt norm for the absolute value c c c 1 2 and the hilbert schmidt norm c hs trc c 1 2 of an operatorc the following inequality is proved for any bounded linear operatorsa andb on a hilbert space a b hs leqq 2 1 2 a b hs the corresponding inequality for two normal state and of a von neumann algebram is also proved in the following form d varphi psi leqq xi varphi xi psi leqq 2 1 2 d varphi psi here denotes the unique vector representative of a state in a natural positive conep form andd denotes the bures distance defined as the infimum which is also the minimum of the distance of vector representatives of and in particular xi varphi 1 xi varphi 2 leqq 2 1 2 xi 1 xi 2 for any vector representatives j of j j 1 2

characterization of the trace by monotonicity inequalities abstract let be a positive linear functional on the algebra of n n complex matrices and p be a number greater than 1 the main result of the paper says that if for any pair a b of positive semi definite n n matrices with a b the inequality a p b p holds true then is a nonnegative scalar multiple of the trace

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

relaxation oscillators with time delay coupling abstract we study networks of relaxation oscillators coupled with time delays synapses a pair of oscillators is analyzed and shown to attain loosely synchronous solutions for a wide range of initial conditions and time delays simulations of one and two dimensional oscillator networks indicate that locally coupled oscillators are also loosely synchronous desynchronous solutions are possible when system parameters are varied to characterize lossely synchronous networks we introduce a measure of synchrony the maximum time difference between any two oscillators in locally excitatory globally inhibitory oscillator networks with time delays we find that desynchronous solutions for different groups of oscillators are maintained and the number of groups that can be segregated is related to the maximum time difference within each group to examine the maximum time difference we display its histograms for oscillator networks in one and two dimensions also a range of initial conditions is given so that the maximum time difference is contained as the system evolves

differentially amplitude and phase encoded qam for the correlated rayleigh fading channel with diversity reception this paper studies the differentially amplitude and phase encoded dape quadrature amplitude modulation qam transmission over correlated rayleigh channels with diversity reception operating over two successive received symbols the optimum and an asymptotic maximum likelihood aml differentially coherent receiver are developed and compared with a conventional switched diversity combining sdc grid receiver it is shown that the aml and sdc grid receivers are much simpler in complexity than the optimum receiver in that no channel side information is required in their realization an exact expression of the bit error probability bep is obtained for the sdc grid receiver based on a union bound argument a bep upper bound for the aml receiver is also derived and verified by simulation numerical results on 16 and 64 point constellations show that the aml receiver exhibits an almost optimum performance and the sdc grid receiver with a small level of diversity is nearly optimum it is also shown by simulation that the conventional equal gain diversity receiver is almost optimal for demodulating a 16 point dape qam signal

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

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

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

amplitude death in an array of limit cycle oscillators we analyze a large system of limit cycle oscillators with mean field coupling and randomly distributed natural frequencies we prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance the system undergoes amplitude death the oscillators pull each other off their limit cycles and into the origin which in this case is astable equilibrium point for the coupled system we determine the region in couplingvariance space for which amplitude death is stable and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system

characterizations of the trace abstract the paper contains a number of equivalent conditions which characterize the trace among the linear functionals on the matrix algebra some of these results are extended to more general operator algebras

coupled chaotic chemical oscillators we present a model study of two mass coupled reactors containing the belousov zhabotinsky reaction under chaotic conditions the critical coupling strength is estimated for symmetry breaking when two identical low flow rate chaotic modes are coupled our results confirm that the critical coupling strength is directly proportional to the maximum lyapunov exponent of the uncoupled system the constant of proportionality is found to be somewhat larger than the theoretical value direct integration reveals a rich structure of dynamical behavior when the coupling strength and the flow rate in one cell are varied our simulations reveal domains of oscillator death in which a stable steady state coexists with limit cycle oscillations we introduce a simple model for predicting the dynamics of the coupled system from the dynamical behavior of the uncoupled subsystems and the dependence on the coupling strength of the hopf bifurcation of the coupled system the model gives good estimates of the dynamical behavior of two coupled oscillators with a small difference in one parameter at intermediate and high coupling strengths textcopyright 1996 the american physical society

global view on a nonlinear oscillator subject to time delayed feedback control we apply time delayed feedback control to stabilise unstable periodic orbits of an amplitude phase oscillator the control acts on both the amplitude and the frequency of the oscillator and we show how the phase of the control signal influences the dynamics of the oscillator a comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop our results provide insight into the global features of time delayed control schemes

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

delayed feedback control of dynamical systems at a subcritical hopf bifurcation we consider the delayed feedback control of a torsion free unstable periodic orbit originated in a dynamical system at a subcritical hopf bifurcation close to the bifurcation point the problem is treated analytically using the method of averaging we discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled system and controller to demonstrate our analytical approach the specific example of a nonlinear electronic circuit is taken as a model of a subcritical hopf bifurcation

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

delayed feedback control of collective synchrony an approach to suppression of pathological brain rhythms we suggest a method for suppression of synchrony in a globally coupled oscillator network based on the time delayed feedback via the mean field having in mind possible applications for suppression of pathological rhythms in neural ensembles we present numerical results for different models of coupled bursting neurons a theory is developed based on the consideration of the synchronization transition as a hopf bifurcation

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

complete chaotic synchronization and exclusion of mutual pyragas control in two delay coupled rossler type oscillators two identical chaotic oscillators that are mutually coupled via time delayed signals show very complex patterns of completely synchronized dynamics including stationary states and periodic as well as chaotic oscillations we have experimentally observed these synchronized states in delay coupled electronic circuits and have analyzed their stability by numerical simulations and analytical calculations we found that the conditions for longitudinal and transversal stability largely exclude each other and prevent e g the synchronization of pyragas controlled orbits most striking is the observation of complete chaotic synchronization for large delay times which should not be allowed in the given coupling scheme on the background of the actual paradigm

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

decision feedback differential detection of differentially encoded 16apsk signals multiple symbol differential detection dd with reference signal estimation based on the feedback of past detected symbols is presented for differentially encoded 16 level amplitude phase shift keying 16dapsk a suboptimal decision is derived the approximate analysis of the bit error rate ber performance taking into account the decision error propagation effect is presented in an additive white gaussian noise awgn channel and the ber performance is compared with those of 16dpsk and 16 quadrature amplitude modulation 16qam

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

adaptive noncoherent linear minimum isi equalization for mdpsk and mdapsk signals a novel noncoherent linear equalization scheme is introduced and analyzed in contrast to previously proposed noncoherent equalization schemes the proposed scheme is not only applicable for m ary differential phase shift keying mdpsk but also for m ary differential amplitude phase shift keying mdapsk the novel scheme minimizes the variance of intersymbol interference isi in the equalizer output signal the optimum equalizer coefficients may be calculated directly from an eigenvalue problem for an efficient recursive adaptation of the equalizer coefficients a modified least mean square lms and a modified recursive least squares rls algorithm are proposed it is shown that the corresponding cost function has no spurious local minima that ensures global convergence of the adaptive algorithms simulations confirm the good performance of the proposed noncoherent equalization scheme and its robustness against frequency offset

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