existence of weak solutions for a hyperbolic model of chemosensitive movement a hyperbolic model for chemotaxis and chemosensitive movement in one space dimension is considered in contrast to parabolic models for chemotaxis the hyperbolic model allows us to take the dependence of the particle speed on external stimuli explicitly into account this qualitatively covers recent experiments on chemotaxis in which it has been shown that particles adapt their speed to the surrounding environment the model presented here consists of two hyperbolic differential equations of first order coupled with an elliptic equation we assume that the speed depends on the external stimulus only and not on its gradients in that case solutions with steep gradients are expected which have the interpretation of moving swarms a notion of weak solutions for this hyperbolic chemotaxis model is presented and the global existence of weak solutions is shown the proof relies on the vanishing viscosity method i e we obtain the weak solution as the limit of classical solutions of an associated parabolically regularized problem for vanishing viscosity parameter numerical simulations demonstrate phenomena like swarming behaviour and formation of steep gradients

individual based model with global competition interaction fluctuation effects in pattern formation we present some numerical results obtained from a simple individual based model that describes clustering of organisms caused by competition our aim is to show that even when a deterministic description developed for continuum models predicts no pattern formation an individual based model displays well defined patterns as a consequence of fluctuation effects caused by the discrete nature of the interacting agents

experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

aggregation blowup and collapse the abc s of taxis in reinforced random walks in many biological systems movement of an organism occurs in response to a diffusible or otherwise transported signal and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by patlak bull of math biophys 15 1953 pp 311 338 however other systems are more accurately modeled by random walkers that deposit a nondiffusible signal that modifies the local environment for succeeding passages in these systems one example of which is the myxobacteria the question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates davis probab theory related fields 84 1990 pp 203 229 has studied this question for a certain class of random walks and here we extend this analysis to the continuum limit of such walks we first derive several general classes of partial differential equations that depend on how the movement rules are

the importance of being discrete life always wins on the surface many systems in chemistry biology finance and social sciences present emerging features that are not easy to guess from the elementary interactions of their microscopic individual components in the past the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions it turns out that to the contrary taking into account the actual individual discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior in fact we find that in conditions in which the continuum approach would predict the extinction of all of the population respectively the vanishing of the invested capital or the concentration of a chemical substance etc the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development in particular it is found that in two dimensions life the localized proliferating phase always prevails

a search for bilinear equations passing hirota s three soliton condition ii mkdv type bilinear equations in this paper the results of a search for complex bilinear equations with two soliton solutions are presented the following basic types are discussed a the nonlinear schrodinger equation b dx g f 0 a dx dt f f gg and b the benjamin ono equation p dx f f 0 it is found that the existence of two soliton solutions is not automatic but introduces conditions that are like the usual three and four soliton conditions the search was limited by the degree of a 2 and by degree of p 4 the main results are the following 1 iad3x dxdt idy b g f 0 d2xf f gg 2 d2x ad2y idt b g f 0 dxdy f f gg 3 iad3x d2x idt f f 0 and 4 dxdt i adx bdt f f 0

four 2 1 dimensional integrable extensions of the kadomtsev petviashvili equation in this work four 2 1 dimensional nonlinear extensions of the kadomtsev petviashvili kp equation are developed the complete integrability of these models are investigated multiple soliton solutions and multiple singular soliton solutions are determined to demonstrate the compatibility of these models the resonance phenomenon does not exist for any of the derived models

multiple soliton solutions for the boussinesq equation abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions for the boussinesq equation the one soliton solutions will be handled by the tanh coth method the work highlights the significant features of the employed methods

demographic fluctuations in a population of anomalously diffusing individuals the phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically the possibility of social behaviors affecting the migration strategies has been taken into exam in the case that anomalous diffusion is produced by means of a continuous time random walk ctrw in the case of independently diffusing individuals the dynamics appears to coincide with that of dying and reproducing brownian walkers in the strongly social case the dynamics coincides with that of nonmigrating individuals in both limits the growth rate of the fluctuations becomes independent of the hurst exponent of the ctrw the social behaviors that arise when transport in a population is induced by a spatial distribution of random traps have been analyzed

kinetics of self induced aggregation of brownian particles non markovian and non gaussian features in this paper we have explored a model for self induced aggregation of brownian particles incorporating non markovian and non gaussian character of the associated random noise processes the time evolution of each individual is guided by an overdamped langevin equation of motion with a nonlocal drift arising out of the imbalance in the local distribution of the other individuals our simulation results show that colored noise enhances the tendency of cluster formation another observation is that the critical noise variance decreases at first with increase in noise correlation time followed by an increase after exhibiting a minimum furthermore in the long time limit the cluster number in the aggregation process exhibits depletion with time following a power law with an exponent which increases remarkably with non markovian character of the noise processes

the hirota s direct method and the tanh coth method for multiple soliton solutions of the sawada kotera ito seventh order equation abstract in this work the sawada kotera ito seventh order equation is studied the tanh coth method is applied to obtain soliton solution of this equation the hirota s direct method combined with the simplified hereman s method are applied to determine the n soliton solutions for this equation the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

regular soliton solutions and singular soliton solutions for the modified kadomtsev petviashvili equations abstract in this paper we study the positive and the negative modified kadomtsev petviashvili mkp equations the mkp equations are completely integrable equations that admit n soliton solutions and an infinite number of conserved densities multiple soliton solutions are obtained for the positive model whereas multiple singular soliton solutions are established for the negative model the analysis depends mainly on the hirota s bilinear method

clustering determines who survives for competing brownian and levy walkers the competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied the latter is assumed to be described either by brownian motion or levy flights competition is taken into account by assuming that individuals reproduce in a density dependent fashion it is observed that no influence of the type of motion occurs when the two species are in a well mixed unstructured state however as soon as the species develop spatial clustering the one forming more concentrated clusters gets a competitive advantage and eliminates the other a similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering the coexistence of both species is also possible under certain conditions

multiple front solutions for the burgers kadomtsev petviashvili equation abstract in this work we study a completely integrable dissipative equation the burgers equation is extended by using the sense of the kadomtsev petviashvili kp equation the new established burgers kp equation is studied by using the tanh coth method to obtain kink solutions and periodic solutions we also apply the powerful hirota s bilinear method to establish exact n soliton solutions for the derived integrable equation

solitons and singular solitons for the gardner kp equation abstract we present in this work a reliable treatment for the gardner kp gkp equation the hirota s bilinear method is used to obtain multiple soliton solutions for this completely integrable equation multiple singular soliton solutions are obtained as well the study highlights a variety of multi solitary wave and multi singular solitary solutions of the gardner kp equation

kinetics of self induced aggregation in brownian particles we study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in a group of individuals each individual represented by a brownian particle experiences an interaction produced by the local unbalance in the spatial distribution of the other individuals this interaction results in a nonlinear velocity driving the particle trajectories in the direction of the nearest more crowded region the competition among different aggregating centers generates nontrivial dynamical regimes our simulations show that for sufficiently low randomness the system evolves through a coalescence behavior characterized by clusters of particles growing with a power law in time in addition the typical scaling properties of the general theory of stochastic aggregation processes are verified

fluctuations impact on a pattern forming model of population dynamics with non local interactions a model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters the model represents biological individuals that die or reproduce at rates depending on the number of neighbors within a given distance we evaluate the importance of the discrete and fluctuating character of this particle model on the pattern forming process to this end a deterministic mean field description including a linear stability and a weakly nonlinear analysis is given and compared with the particle model the deterministic approach is shown to reproduce some of the features of the discrete description in particular the existence of a finite wavelength instability stochasticity in the particle dynamics however has strong effects in other important aspects such as the parameter values at which pattern formation occurs or the nature of the homogeneous phase

pattern formation and nonlocal logistic growth logistic growth process with nonlocal interactions is considered in one dimension spontaneous breakdown of translational invariance is shown to take place at some parameter region and the bifurcation regime is identified for short and long range interactions domain walls between regions of different order parameter are expressed as soliton solutions of the reduced dynamics for nearest neighbor interactions the analytic results are confirmed by numerical simulations

a note on multivariable generalized predictive control this note presents a stability result for the multivariable version of the generalized predictive control algorithm shah et al 1989 in particular closed loop stability is obtained for any open loop asymptotically stable plant by a proper selection of the future output horizon and of the control weighting matrix the control law contains an integral action thus guaranteeing regulation with zero steady state error for constant exogeneous signals

clustering and coalescence from multiplicative noise the kraichnan ensemble we study the dynamics of the two point statistics of the kraichnan ensemble which describes the transport of a passive pollutant by a stochastic turbulent flow characterized by scale invariant structure functions the fundamental equation of this problem consists of the fokker planck equation for the two point correlation function of the density of particles performing spatially correlated brownian motions with scale invariant correlations this problem is equivalent to the stochastic motion of an effective particle driven by a generic multiplicative noise in this paper we propose an alternative and more intuitive approach to the problem than the original one gawedzki and vergassola 2000 physica d 138 63 leading to the same conclusions the general features of this new approach make possible to fit it to other more complex contexts

multiple front solutions for the burgers equation and the coupled burgers equations abstract in this work multiple front solutions for the burgers equation and the coupled burgers equations are examined the tanh coth method and the cole hopf transformation are used the work highlights the power of the proposed schemes and the structures of the obtained multiple front solutions

influence of noise on the synchronization of the stochastic kuramoto model we consider the kuramoto model of globally coupled phase oscillators subject to ornstein uhlenbeck and non gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process we use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise and find that the threshold of synchronization strongly depends on the nature of the noise it is found to be lower for both the ornstein uhlenbeck and non gaussian processes compared to the case of white noise a finite correlation time also favors the achievement of the full synchronization of the system in contract to the white noise process which does not allow that finally we discuss possible applications of the stochastic kuramoto model to oscillations taking place in biochemical systems

macroscopic model of self propelled bacteria swarming with regular reversals periodic reversals in the direction of motion in systems of self propelled rod shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize the swarming rate of the colony in this paper a connection is established between a microscopic one dimensional cell based stochastic model of reversing nonoverlapping bacteria and a macroscopic nonlinear diffusion equation describing the dynamics of cellular density boltzmann matano analysis is used to determine the nonlinear diffusion equation corresponding to the specific reversal frequency stochastic dynamics averaged over an ensemble is shown to be in very good agreement with the numerical solutions of this nonlinear diffusion equation critical density p0 is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities p p0 an analytical approximation of the pairwise collision time and semianalytical fit for the total jam time per reversal period are also obtained it is shown that cell populations with high reversal frequencies are able to spread out effectively at high densities if the cells rarely reverse then they are able to spread out at lower densities but are less efficient at spreading out at higher densities

point processes and stochastic displacement fields the effect of a stochastic displacement field on a statistically independent point process is analyzed stochastic displacement fields can be divided into two large classes spatially correlated and uncorrelated for both cases exact transformation equations for the two point correlation function and the power spectrum of the point process are found and a detailed study of them with important paradigmatic examples is done the results are general and in any dimension particular attention is devoted to the kind of large scale correlations that can be introduced by the displacement field and to the realizability of arbitrary superhomogeneous point processes

role of phase difference and colored cross correlation on current in multiplicative and additive noises driven systems abstract we have investigated the transport properties of multiplicative and additive noise driven spatially periodic system the phase difference between periodic potential and periodic function in multiplicative noise term and the cross correlation between multiplicative and additive noise can break the detail balance of the system independently to produce directed motion the magnitude of current due to phase difference is smaller in comparison to cross correlation between the noises the phase difference can be used to control the direction of the cross correlation induced current another interesting observation is that there is a current inversion with increase of cross correlation time the current increases linearly with the strength of cross correlation

theory of neutral clustering for growing populations the spatial distribution of most species in nature is nonuniform we have shown recently b houchmandzadeh phys rev lett 101 078103 2008 on an experimental ecological community of amoeba that the most basic facts of life birth and death are enough to cause considerable aggregation which cannot be smoothened by random movements of the organisms this clustering termed neutral and always present is independent of external causes and social interaction we develop here the theoretical groundwork of this phenomenon by explicitly computing the pair correlation function and the variance to mean ratio of the above neutral model and its comparison to numerical simulations

algebraic geometrical solutions of some multidimensional nonlinear evolution equations the known 2 1 dimensional breaking soliton equation the coupled kp equation with three potentials and a new 3 1 dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the 1 1 dimensional akns equations the abel jacobi coordinates are introduced to straighten out the associated flows from which algebraic geometrical solutions of the 2 1 dimensional breaking soliton equation the coupled kp equation and the 3 1 dimensional evolution equation are explicitly given in terms of the riemann theta functions

heavy particles in incompressible flows the large stokes number asymptotics abstract the dynamics of very heavy particles suspended in incompressible flows is studied in the asymptotics in which their response time is much larger than any characteristic time of fluid motion in this limit of very large stokes numbers particles behave as if suspended in a correlated in time gaussian flow at those spatial scales where the fluid velocity field is smooth following piterbarg l i piterbarg the top lyapunov exponent for stochastic flow modeling the upper ocean turbulence siam j appl math 62 2002 777 and mehlig et al b mehlig m wilkinson k duncan t weber m ljunggren aggregation of inertial particles in random flows phys rev e 72 2005 051104 the two particle dynamics is reduced to a nonlinear system of three stochastic differential equations with additive noise this model is used to single out the mechanisms leading to the preferential concentration of particles scaling arguments are used to predict the large stokes number behavior of the distribution of the stretching rate and of the probability distribution function of the longitudinal velocity difference between two particles as for the fractal character of the particle distribution strong numerical evidence is obtained in favor of saturation of the correlation dimension to the space dimension at large stokes numbers numerical results at finite stokes number values reveal that this model catches some important qualitative features of particle clustering observed in more realistic flows

nonlocal competition and logistic growth patterns defects and fronts logistic growth of diffusing reactants on spatial domains with long range competition is studied the bifurcations cascade involved in the transition from the homogeneous state to a spatially modulated stable solution is presented and a distinction is made between a modulated phase dominated by single or few wave numbers and the spiky phase where localized colonies are separated by depleted region the characteristic defects in the periodic structure are presented for each phase together with the invasion dynamics in the case of local initiation it is shown that the basic length scale that controls the bifurcation is the width of the fisher front and that the total population grows as this width decreases a mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition

nature of different types of absorbing states we present a comparison of three different types of langevin equations exhibiting absorbing states the langevin equation defining the reggeon field theory one with multiplicative noise and a third type in which the noise is complex each one is found to describe a different underlying physical mechanism in particular the nature of the different absorbing states depends on the type of noise considered by studying the stationary single site effective potential we analyze the impossibility of finding a reaction diffusion model in the multiplicative noise universality class we also discuss some theoretical questions related to the nature of complex noise as for example whether it is necessary or not to consider a complex equation in order to describe processes as the annihilation reaction a stackrel ensuremath rightarrow a 0

the hirota s direct method for multiple soliton solutions for three model equations of shallow water waves abstract multiple soliton solutions for three model equations for shallow water waves are determined the three models are completely integrable the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these equations the tanh coth method is used to obtain single soliton solutions and other solutions for these three models the three models have different linear dispersion relations but possess the same coefficients for the polynomials of exponentials

competitive brownian and levy walkers population dynamics of individuals undergoing birth and death and diffusing by short or long range two dimensional spatial excursions gaussian jumps or l evy flights is studied competitive interactions are considered in a global case in which birth and death rates are influenced by all individuals in the system and in a nonlocal but finite range case in which interaction affects individuals in a neighborhood we also address the noninteracting case in the global case one single or few cluster configurations are achieved with the spatial distribution of the bugs tied to the type of diffusion in the l evy case long tails appear for some properties characterizing the shape and dynamics of clusters under nonlocal finite range interactions periodic patterns appear with periodicity set by the interaction range this length acts as a cutoff limiting the influence of the long l evy jumps so that spatial configurations under the two types of diffusion become more similar by dividing initially everyone into different families and following their descent it is possible to show that mixing of families and their competition is greatly influenced by the spatial dynamics

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

robust ecological pattern formation induced by demographic noise we demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the levin segel predator prey model for plankton herbivore population dynamics although the model exhibits a turing instability in mean field theory demographic noise greatly enlarges the region of parameter space where pattern formation occurs to distinguish between patterns generated by fluctuations and those present at the mean field level in real ecosystems we calculate the power spectrum in the noise driven case and predict the presence of fat tails not present in the mean field case these results may account for the prevalence of large scale ecological patterns beyond that expected from traditional nonstochastic approaches

multiple soliton solutions for the lax kadomtsev petviashvili lax kp equation a new completely integrable dispersive equation is derived the new equation is obtained by extending the lax fifth order equation using the sense of the kadomtsev petviashvili kp equation in extending the kdv equation the newly derived lax kadomtsev petviashvili lax kp equation is investigated by using the tanh coth method and the hirota bilinear method to derive single soliton solution and n soliton solutions respectively the study highlights the multiple soliton solutions of the derived completely integrable equation

a parameter optimization approach to the design of structurally constrained regulators for discrete time systems the problem dealt with in this paper is the design of a regulator for a discrete time system the regulator should impose a satisfactory dynamic behaviour on the overall control system and guarantee robust zero error regulation for constant exogenous signals the technique presented here is based on parameter optimization and being very flexible is particularly suited to cope with various constraints which may be imposed on the structure of the regulator for example decentralization of the overall regulation system and the order of the local devices the design problem is stated first as an optimal control problem its reformulation as a mathematical programming problem is then presented with some computational remarks the effectiveness of the proposed technique is verified by two illustrative examples

flows coalescence and noise we are interested in stationary fluid random evolutions with independent increments under some mild assumptions we show they are solutions of a stochastic differential equation sde there are situations where these evolutions are not described by flows of diffeomorphisms but by coalescing flows or by flows of probability kernels in an intermediate phase for which there exist a coalescing flow and a flow of kernels solution of the sde a classification is given all solutions of the sde can be obtained by filtering a coalescing motion with respect to a subnoise containing the gaussian part of its noise thus the coalescing motion cannot be described by a white noise

quasi periodic solutions for some 2 1 dimensional integrable models generated by the jaulent miodek hierarchy some 2 1 dimensional integrable models including the modified kadomtsev petviashvili equation generated by the jaulent miodek hierarchy are investigated with the help of the jaulent miodek eigenvalue problem these 2 1 dimensional integrable models are separated into compatible hamiltonian systems of ordinary differential equations using the generating function flow method the involutivity and the functional independence of the integrals are proved the abel jacobi coordinates are introduced from which the quasi periodic solutions for these 2 1 dimensional integrable models are derived by resorting to the riemann theta functions pacs number 0230j

multiple soliton solutions of two extended model equations for shallow water waves abstract multiple soliton solutions for two extensions of model equations for shallow water waves presented in m j ablowitz d j kaup a c newell h segur the inverse scattering transform fourier analysis for nonlinear problems stud appl math 53 1974 249 315 r hirota j satsuma n soliton solutions of model equations for shallow water waves j phys soc jpn 40 2 1976 611 612 are obtained the two extensions possess identical dispersion relations but with different structures for the n soliton solutions for n 1 the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these extended equations the tanh coth method is used to obtain single soliton solutions

rate laws of the self induced aggregation kinetics of brownian particles abstract in this paper we have studied the self induced aggregation kinetics of brownian particles in the presence of both multiplicative and additive noises in addition to the drift due to the self aggregation process the environment may induce a drift term in the presence of a multiplicative noise then there would be an interplay between the two drift terms it may account qualitatively the appearance of the different laws of aggregation process at low strength of white multiplicative noise the cluster number decreases as a gaussian function of time if the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time for additive noise driven case the decrease of cluster number can be described by the power law but in case of multiplicative colored driven process cluster number decays multi exponentially however we have explored how the rate constant in the mono exponentially cluster number decaying case depends on strength of interference of the noises and their intensity we have also explored how the structure factor at long time depends on the strength of the cross correlation cc between the additive and the multiplicative noises

multiple kink solutions and multiple singular kink solutions for the 2 1 dimensional burgers equations abstract in this work we study the 2 1 dimensional painleve integrable burgers equation multiple kink solutions and multiple singular kink solutions are formally derived for this equation the analysis depends mainly on the hirota s bilinear method

interplay of chemotaxis and chemokinesis mechanisms in bacterial dynamics motivated by observations of the dynamics of myxococcus xanthus we present a self interacting random walk model that describes the competition between chemokinesis and chemotaxis cells are constrained to move in one dimension but release a chemical chemoattractant at a steady state the bacteria sense the chemical that they produce the probability of direction reversals is modeled as a function of both the absolute level of chemoattractant sensed directly under each cell as well as the gradient sensed across the length of the cell if the chemical does not degrade or diffuse rapidly the one dimensional trajectory depends on the entire past history of the trajectory we derive the corresponding fokker planck equations use an iterative mean field approach that we solve numerically for short times and perform extensive monte carlo simulations of the model cell positional distributions and the associated moments are computed in this feedback system average drift and mean squared displacements are found crossover behaviors among different diffusion regimes are found

randomly curved runs interrupted by tumbling a model for bacterial motion received 23 february 2005 published 24 august 2005small bacteria are strongly buffeted by brownian forces that make completely straight runs impossible amodel for bacterial motion is formulated in which the effects of uctuational forces and torques on the runphase are taken into account by using coupled langevin equations an integrated description of the motion including runs and tumbles is then obtained by the use of convolution and laplace transforms the propertiesof the velocity velocity correlation function of the mean displacement and of the two relevant diffusioncoef cients are examined in terms of the bacterial sizes and of the magnitude of the propelling forces forbacteria smaller than

a cellular automata model of flow in ant trails non monotonic variation of speed with density generically in models of driven interacting particles the average speed of the particles decreases monotonically with increasing density we propose a counterexample motivated by the motion of ants in a trail where the average speed of the particles varies non monotonically with their density because of the coupling of their dynamics with another dynamical variable these results in principle can be tested experimentally

a multivariable self tuning controller with integral action abstract in this paper a novel stochastic self tuning control algorithm for multivariable linear systems described by controlled autoregressive integrating moving average carima models is proposed in particular the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant the leading assumption is made that the system interactor matrix is known a priori the algorithm is derived by resorting to the generalized minimum variance approach two simulation examples illustrate the main features of the method

multivariable adaptive control without a prior knowledge of the delay matrix this paper is concerned with the structure and role of the time delay matrix in discrete time multivariable processes interpretations and properties of this matrix as a multivariable generalization of the siso delay term are discussed it is formally shown that a finite time horizon or multi step cost function for the multivariable case can be minimized subject to a suitable choice of output and control horizons and without prior knowledge of the system delay matrix

multiple soliton solutions for the kp equation by hirota s bilinear method and by the tanh coth method abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions n 1 2 3 4 5 for the kadomtsev petviashvili kp equation the one soliton solutions will be handled by the tanh coth method the work emphasizes the power of the two methods that will be used

a numerical solution and an exact explicit solution of the nls equation we consider traveling wave solutions of the nonlinear schrodinger nls for short equation in this paper by considering the decomposition scheme we first obtain the exact solutions of the nls equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some initial values of the nls equation

diffusion reproduction processes interesting physics emerges from studying a population of reproducing individuals each can be regarded as a random walker but it can either duplicate or die novel features of the collective behavior are quite surprising if individuals reproduce or die freely the life expectation is proportional to the size of the population and if it is kept constant the center of mass moves in space as if it were a single walker i e the diffusion constant is independent of population s size biology inspired interactions are also considered

macroscopic description of particle systems with nonlocal density dependent diffusivity in this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself we show that large differences not present in the local densitydependence case appear between the density equations that are derived from different representations of the langevin equation describing a system of interacting brownian particles linear stability analysis demonstrates that under some circumstances the density equation interpreted with the ito calculus has pattern solutions that never appear for the kinetic interpretation which is the other one typically appearing in the context of nonlinear diffusion processes we also introduce a discrete time microscopic model of particles that confirms the results obtained at the macroscopic density level