hopf bifurcation and stability for a differential algebraic biological economic system abstract in this paper we analyze the stability and hopf bifurcation of the biological economic system based on the new normal form and the hopf bifurcation theorem the basic model we consider is owed to a ratio dependent predator prey system with harvesting compared with other researches on dynamics of predator prey population this system is described by differential algebraic equations due to economic factor here as bifurcation parameter it is found that periodic solutions arise from stable stationary states when the parameter increases close to a certain limit finally numerical simulations illustrate the effectiveness of our results

copula based daily rainfall disaggregation model 1 a daily rainfall disaggregation model which uses a copula to model the dependence structure between total depth total duration of wet periods and the maximum proportional depth of a wet period is presented the wet 1 dry 0 binary sequence is modeled by the nonrandomized bartlett lewis model with diurnal effect incorporated before superimposing the ar 1 depth process submodel unlike previous studies the model is structured such that all wet day data available are considered in the analysis without the need to discard any good quality daily data embedded in a month having some missing data this increased the data size thus improving the modeling process further the daily data are classified according to the total duration of wet periods duration within the day in this way a large proportion of the model parameters become seasonal invariant the overriding factor being the total duration of wet periods the potential of the developed model has been demonstrated by disaggregating both the data set used in developing the model parameters and also a 12 year continuous rainfall data set not used in the model parameterization gross rainfall statistics of several aggregation levels down to 6 min have been very well reproduced by the disaggregation model the copula dependence structure and the variation of the depth process submodel parameters with the total duration of wet periods are also very well captured by the presented model

ldpc codes based on latin squares cycle structure stopping set and trapping set analysis it is well known that certain combinatorial structures in the tanner graph of a low density parity check ldpc code exhibit a strong influence on its performance under iterative decoding these structures include cycles stopping trapping sets and parameters such as the diameter of the code in general it is very hard to find a complete characterization of such configurations in an arbitrary code and even harder to understand the intricate relationships that exist between these entities it is therefore of interest to identify a simple setting in which all the described combinatorial structures can be enumerated and studied within a joint framework one such setting is developed in this paper for the purpose of analyzing the distribution of short cycles and the structure of stopping and trapping sets in tanner graphs of ldpc codes based on idempotent and symmetric latin squares the parity check matrices of ldpc codes based on latin squares have a special form that allows for connecting combinatorial parameters of the codes with the number of certain subrectangles in the latin squares subrectangles of interest can be easily identified and in certain instances completely enumerated this study can be extended in several different directions one of which is concerned with modifying the code design process in order to eliminate or reduce the number of configurations bearing a negative influence on the performance of the code another application of the results includes determining to which extent a configuration governs the behavior of the bit error rate curve in the waterfall and error floor regions

a spatial temporal point process model with a continuous distribution of storm types 1 a point process rainfall model is further developed that has storm origins occurring in space time according to a poisson process where each storm origin has a random radius so that storms occur as circular regions in two dimensional space where the storm radii are taken to be independent exponential random variables each storm origin is of random type z where z follows a continuous probability distribution cell origins occur in a further spatial poisson process and have arrival times that follow a neyman scott point process each cell origin has a radius so that cells form discs in two dimensional space where the cell radii are independent exponential random variables each cell has a random lifetime and an intensity that remains constant over both the cell lifetime and cell disk area statistical properties up to third order are given for the model using these properties the model is fitted to 10 min series taken from 23 sites across the rome region italy distributional properties of the observed annual maxima are compared to equivalent values sampled from series that are simulated using the fitted model the results indicate that the model will be of use in urban drainage projects for the rome region

bifurcation and chaotic behavior of a discrete singular biological economic system abstract in this paper the complex dynamics of a discrete singular biological economic system are first investigated firstly we establish a discrete singular biological economic system which is based on the discretization of a differential algebraic equations that is described by a ratio dependent predator prey system with harvesting and economic factor then it is shown that the system undergoes flip bifurcation and neimark sacker bifurcation in the interior of r 3 by using the new normal form of discrete singular systems the center manifold theorem and the bifurcation theory as varying the economic profit in some range numerical simulations are presented not only to illustrate our results with the theoretical analysis but also to exhibit the complex dynamic behaviors such as cascades of period doubling bifurcation in orbits of period 2 4 8 and chaotic sets these results reveal far richer dynamics of the discrete model compared with the continuous model the lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors

optimal control of switched systems based on parameterization of the switching instants this paper presents a new approach for solving optimal control problems for switched systems we focus on problems in which a prespecified sequence of active subsystems is given for such problems we need to seek both the optimal switching instants and the optimal continuous inputs in order to search for the optimal switching instants the derivatives of the optimal cost with respect to the switching instants need to be known the most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state costate stationarity equations the boundary and continuity conditions along with their differentiations this method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed an extension of the method is also applied to problems with internally forced switching examples are shown to illustrate the results in the paper

oscillations fluctuation intensity and optimal harvesting of a bio economic model in a complex habitat abstract we investigate the effects of habitat complexity and multi time delays on dynamics of a bio economic predator prey model the differential algebraic system theory is applied to transform the bio economic model into a normal form so that the local stability and existence of periodic solutions can be examined by varying the delays and the habitat complexity parameter the direction of hopf bifurcation and the stability of bifurcated periodic solutions are investigated we also discuss the effect of fluctuating environment on dynamical behavior of a corresponding stochastic delayed differential algebraic system and derive expressions for intensities of population fluctuations the model is also used to study the optimal harvesting strategy in order to maximize economic profit while sustaining the ecosystem numerical simulations are designed to illustrate the effectiveness of theoretical analysis

algebraic construction of quasi cyclic ldpc codes for the awgn and erasure channels this paper is concerned with construction of quasi cyclic qc low density parity check ldpc codes for three different types of channels the additive white gaussian noise the binary random erasure and the binary burst erasure channels two algebraic methods for systematic construction of qc ldpc codes are presented codes constructed perform well over all three types of channels

quasi cyclic ldpc codes an algebraic construction this paper presents two new large classes of qc ldpc codes one binary and one non binary codes in these two classes are constructed by array dispersions of row distance constrained matrices formed based on additive subgroups of finite fields experimental results show that codes constructed perform very well over the awgn channel with iterative decoding based on belief propagation codes of a subclass of the class of binary codes have large minimum distances comparable to finite geometry ldpc codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low complexity reliability based iterative decoding algorithms such as binary message passing decoding algorithms non binary codes decoded with a fast fourier transform based sum product algorithm achieve significantly large coding gains over reed solomon codes of the same lengths and rates decoded with either the hard decision berlekamp massey algorithm or the algebraic soft decision kotter vardy algorithm they have potential to replace reed solomon codes in some communication or storage systems where combinations of random and bursts of errors or erasures occur

stability and further analytical bifurcation behaviors of moran ricker model with delayed density dependent birth rate regulation abstract in this paper we consider moran ricker model with delayed density dependent birth rate presented by neverova et al 2016 it is well known that normal form of a dynamical system is easier to work with while it has the same qualitative properties as those of the original one firstly existence and local stability analysis of the model fixed points are addressed then normal form theory and perturbation method are applied to investigate different types of bifurcations included in the model it is demonstrated the presence of transcritical flip and neimark sacker bifurcations in the model in addition it is proved that the model has a chaotic behavior in the sense of marotto finally numerical simulations are provided to verify our analytic results compared with those obtained in neverova et al 2016 and explore further rich dynamics of the model as well

derived flood frequency distribution for negatively correlated rainfall intensity and duration derived flood frequency distributions dffd are relatively new in the field of hydrology these models use rainfall and catchment characteristics for deriving the flood frequency distribution the dffd models developed so far use joint probability density function of exponentially distributed rainfall intensity and duration and consider these variables as independent of each other in reality this may not be true and these variables may be correlated as well in the present paper a physically based flood frequency model has been developed for negatively correlated rainfall intensity and duration in the model infiltration losses are represented by the index the geomorphoclimatic instantaneous unit hydrograph gciuh is used as the effective rainfall runoff model

regular and irregular progressive edge growth tanner graphs we propose a general method for constructing tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge by edge manner called progressive edge growth peg algorithm lower bounds on the girth of peg tanner graphs and on the minimum distance of the resulting low density parity check ldpc codes are derived in terms of parameters of the graphs simple variations of the peg algorithm can also be applied to generate linear time encodeable ldpc codes regular and irregular ldpc codes using peg tanner graphs and allowing symbol nodes to take values over gf q q 2 are investigated simulation results show that the peg algorithm is a powerful algorithm to generate good short block length ldpc codes

further developments of the neyman scott clustered point process for modeling rainfall this paper provides some useful results for modeling rainfall it extends work on the neyman scott cluster model for simulating rainfall time series several important properties have previously been found for the model for example the expectation and variance of the amount of rain captured in an arbitrary time interval rodriguez iturbe et al 1987a in this paper additional properties are derived such as the probability of an arbitrary interval of any chosen length being dry in applications this is a desirable property to have and is often used for fitting stochastic rainfall models to field data the model is currently being used in rainfall time series research directed toward improving sewage systems in the united kingdom to illustrate the model s performance an example is given where the model is fitted to 10 years of hourly data taken from blackpool england

construction of non binary quasi cyclic ldpc codes by arrays and array dispersions transactions papers this paper presents two algebraic methods for constructing high performance and efficiently encodable nonbinary quasi cyclic ldpc codes based on arrays of special circulant permutation matrices and multi fold array dispersions codes constructed based on these methods perform well over the awgn and other types of channels with iterative decoding based on belief propagation experimental results show that over the awgn channel these non binary quasi cyclic ldpc codes significantly outperform reed solomon codes of the same lengths and rates decoded with either algebraic hard decision berlekamp massey algorithm or algebraic soft decision kotter vardy algorithm also presented in this paper is a class of asymptotically optimal ldpc codes for correcting bursts of erasures codes constructed also perform well over flat fading channels non binary quasi cyclic ldpc codes have a great potential to replace reed solomon codes in some applications in communication environments and storage systems for combating mixed types of noises and interferences

quasicyclic low density parity check codes from circulant permutation matrices in this correspondence the construction of low density parity check ldpc codes from circulant permutation matrices is investigated it is shown that such codes cannot have a tanner graph representation with girth larger than 12 and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived these results suggest that families of ldpc codes with such girth values are relatively easy to obtain and consequently additional parameters such as the minimum distance or the number of redundant check sums should be considered to this end a necessary condition for the codes investigated to reach their maximum possible minimum hamming distance is proposed

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

brief paper minimax state estimation for linear discrete time differential algebraic equations this paper presents a state estimation approach for an uncertain linear equation with a non invertible operator in hilbert space the approach addresses linear equations with uncertain deterministic input and noise in the measurements which belong to a given convex closed bounded set a new notion of a minimax observable subspace is introduced by means of the presented approach new equations describing the dynamics of a minimax recursive estimator for discrete time non causal differential algebraic equations daes are presented for the case of regular daes it is proved that the estimator s equation coincides with the equation describing the seminal kalman filter the properties of the estimator are illustrated by a numerical example

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

fitting bivariate copulas to the dependence structure between storm characteristics a detailed analysis based on 105 year 10 min rainfall 1 the use of copulas as flexible tools for constructing marginal free distribution functions for multivariate phenomena such as rainfall recently enjoys substantial attention by researchers in hydrology in this study commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall observed at uccle belgium in the analysis various problems that can occur are highlighted and opportunities for further research are outlined after selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data a detailed seasonal dependence analysis is provided together with a study on tail dependence further different existing parameter estimation techniques and goodness of fit methods for selecting the most appropriate bivariate copulas are applied and compared finally attention is given to the presence of asymmetric dependence and nonexchangeability

a comparative copula based bivariate frequency analysis of observed and simulated storm events a case study on bartlett lewis modeled rainfall 1 because of a lack of historical rainfall time series of considerable length one often has to rely on simulated rainfall time series e g in the design of hydraulic structures one way to simulate such time series is by means of stochastic point process rainfall models such as the bartlett lewis type of model for the evaluation of model performance with a focus on the reproduction of extreme rainfall events often a univariate extreme value analysis is performed recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models in this study a copula based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms first this study performs an analysis of several storm variables which indicates a problem with the modeling of the temporal structure of rainfall by the models thereafter the bivariate frequency analysis of storms defined by their duration and volume illustrates the underestimation and overestimation of the return period of the storms simulated by the models which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume the difference in the degree of association between the latter and a different mean storm interarrival time the proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made

further investigations into the stability and bifurcation of a discrete predator prey model abstract in this paper we revisit a discrete predator prey model with a non monotonic functional response originally presented in hu teng and zhang 2011 6 first by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points e 3 and e 4 obtained in this article we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria here we present a very useful lemma which is a corrected version of a known result and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system we then study the stability and bifurcation for the equilibrium point e 1 of this system which has not been considered in any known literature unlike known results that present a large number of mathematical formulae that are not easily verified we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation which are explicitly expressed by the coefficient of the system the center manifold theory and project method are the main tools in the analysis of bifurcations the theoretical results obtained are further illustrated by numerical simulations

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

shortened array codes of large girth one approach to designing structured low density parity check ldpc codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity check matrix contain all the variables involved in short cycles this approach is especially effective if the parity check matrix of a code is a matrix composed of blocks of circulant permutation matrices as is the case for the class of codes known as array codes we show how to shorten array codes by deleting certain columns of their parity check matrices so as to increase their girth the shortening approach is based on the observation that for array codes and in fact for a slightly more general class of ldpc codes the cycles in the corresponding tanner graph are governed by certain homogeneous linear equations with integer coefficients consequently we can selectively eliminate cycles from an array code by only retaining those columns from the parity check matrix of the original code that are indexed by integer sequences that do not contain solutions to the equations governing those cycles we provide ramsey theoretic estimates for the maximum number of columns that can be retained from the original parity check matrix with the property that the sequence of their indices avoid solutions to various types of cycle governing equations this translates to estimates of the rate penalty incurred in shortening a code to eliminate cycles simulation results show that for the codes considered shortening them to increase the girth can lead to significant gains in signal to noise ratio snr in the case of communication over an additive white gaussian noise awgn channel

probabilistic representation of the temporal rainfall process by a modified neyman scott rectangular pulses model parameter estimation and validation the capability of the neyman scott clustered stochastic point process model of rainfall to preserve various observed statistics is considered randomization of the cell duration parameter from storm to storm is shown to considerably improve the wet dry period joint distribution and extreme value statistics a simple procedure for parameter estimation is introduced and applied

permanence and stability of a predator prey system with stage structure for predator a stage structured predator prey system with delays for prey and predator respectively is proposed and analyzed mathematical analysis of the model equations with regard to boundedness of solutions permanence and stability are analyzed some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium respectively are obtained

a new rainfall model based on the neyman scott process using cubic copulas 1 a classical way to model rainfall is to use a poisson process authors generally employed cluster of rectangular pulses to reproduce the hierarchical structure of rainfall storms although independence between cell intensity and duration turned out to be a nonrealistic assumption only a few models link these variables in this paper a neyman scott cluster process considering dependence between cell depth and duration is developed we introduce this link with a cubic copula copulas are multivariate distributions modeling the dependence structure between variables preserving the marginal distributions thanks to this flexibility we are able to introduce a global concept of dependence between cell depth and duration we derive the aggregated moments first second and third order moments from the new model for several families of polynomial copulas and perform an application on belgium and american data

two reliability based iterative majority logic decoding algorithms for ldpc codes this paper presents two novel reliability based iterative majority logic decoding algorithms for ldpc codes both algorithms are binary message passing algorithms and require only logical operations and integer additions consequently they can be implemented with simple combinational logic circuits they either outperform or perform just as well as the existing weighted bit flipping or other reliability based iterative decoding algorithms for ldpc codes in error performance with a faster rate of decoding convergence and less decoding complexity compared to the sum product algorithm for ldpc codes they offer effective trade offs between performance and decoding complexity

quasi cyclic ldpc codes an algebraic construction rank analysis and codes on latin squares quasi cyclic ldpc codes are the most promising class of structured ldpc codes due to their ease of implementation and excellent performance over noisy channels when decoded with message passing algorithms as extensive simulation studies have shown in this paper an approach for constructing quasi cyclic ldpc codes based on latin squares over finite fields is presented by analyzing the parity check matrices of these codes combinatorial expressions for their ranks and dimensions are derived experimental results show that with iterative decoding algorithms the constructed codes perform very well over the awgn and the binary erasure channels