coupled map lattices with complex order parameter abstract we introduce and study coupled map lattices with complex state variable the dynamical regimes of the finite length systems are classified naturally in terms of a topological invariant the overall phase shift accumulated along the whole length at fixed time a stability analysis of the spatially uniform states is presented and the results of numerical simulations of the spatio temporal dynamics are discussed we demonstrate that fast amplitude evolution including regular and chaotic spatio temporal behavior takes place on the background of a slower phase evolution for large values of the topological invariant the phase dynamics may give rise to an instability which in some cases results in a jump of the system to another value of the invariant we also consider the formation of long lived bubbles i e local domains of complicated dynamics in the spatial regions of locally reduced phase gradient our coupled map lattice model and its generalizations may be useful for understanding the dynamics in a larger range of parameters for such nonlinear dissipative media which allow small amplitude description in terms of the complex ginzburg landau equation as well as for time delay feedback systems with nonzero central frequency of the generated signal

asymptotic stability of densities in coupled map lattices abstract sufficient conditions for the asymptotic stability strong convergence of density evolution in finite dimensional piecewise monotone map lattices with both constant and state dependent coupling are given these conditions are quite useful in numerical work since they allow one to precisely define where one expects to see numerical signatures of asymptotic stability asymptotic stability is illustrated with several examples it is also shown that in constantly coupled lattices the density formed by collapsing the higher dimensional density into one dimension can be approximated by the evolution of densities under the action of an appropriately perturbed one dimensional map

hukuhara differentiability of interval valued functions and interval differential equations on time scales abstract using the concept of the generalized hukuhara difference in this paper we introduce and study the differentiability and the integrability for the interval valued functions on time scales some illustrative examples to interval differential equations on time scales are presented

set valued functions in frechet spaces continuity hukuhara differentiability and applications to set differential equations abstract the set k c f of compact convex subsets of a frechet space f is studied in detail and is realized as a projective limit of metric spaces the notion of hausdorff metric on it is replaced by a family of corresponding semi metrics which provide the necessary background for the support of continuity and lipschitz continuity finally the notion of hukuhara derivative suited to our study is developed the proposed approach forms the appropriate environment within which the study of set differential equations for frechet spaces can be developed a first example on r is included

fractional calculus for interval valued functions abstract we use a generalization of the hukuhara difference for closed intervals on the real line to develop a theory of the fractional calculus for interval valued functions the properties of riemann liouville fractional integral riemann liouville fractional derivative and caputo fractional derivative for interval valued functions are investigated several examples are presented to illustrate the concepts and results

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

stochastic system with colored correlation between white noise and colored noise abstract a stochastic system with colored correlation between white noise and colored noise is investigated theoretically a general fokker planck equation of the system is derived by using a standard method we discuss a bistable system with colored correlation between additive white noise and multiplicative colored one it is found that the effects of the correlation time of multiplicative colored noise on the statistical properties of the bistable system are different from those of the correlation time of the correlation between additive white noise and multiplicative colored noise on the statistical properties of the bistable system

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

fuzzy fractional functional integral and differential equations this paper is devoted to considering the existence and uniqueness results for fuzzy fractional functional integral equations employing the contraction principle moreover the approach is followed to prove the existence and uniqueness of solutions for the fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives finally the solution to fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives by a modified fractional euler method mfem is presented the method is illustrated by solving some examples

on the stability of fuzzy dynamical systems abstract in this work we study the asymptotic behavior of fuzzy solutions obtained by using zadeh s extension at the deterministic solutions of initial value problems we obtain some result regarding the existence of fuzzy equilibrium points that generalize the already known results as show earlier the membership function of the fuzzy equilibrium points may be obtained in a relatively simple way also we study the projection of the fuzzy solution on the appropriate subspaces of the phase space several examples are given to illustrate the obtained results

pattern selection at high nonlinearity in a diffusively coupled logistic lattice a different pattern selection regime is shown to exist in regions of high nonlinearity in the diffusively coupled logistic lattice with nearest neighbor interaction for this regime the phase diagram of several prominent attractors is determined the results indicate that the spatiotemporal chaos in some of the regions so far believed to be areas of fully developed spatiotemporal chaos is of a transient nature

spatiotemporal chaos in a coupled map lattice with unstable couplings we study the complex spatiotemporal behaviour of a coupled map lattice with a one humped chaotic map and an unstable laplacian coupling bifurcations are numerically investigated and interpreted using low dimensional approximations corresponding to the relevant degrees of freedom of the infinite dimensional system varying the control parameter we find different phases in the chaotic domain such as localized chaos or propagating chaos spatiotemporal intermittency and transient chaos according to our results unstable coupling leads to a number of new features including the effects that i the first bifurcation becomes discontinuous and ii the chaotic regime sets in sooner than for a single map

transient spatiotemporal chaos is extensive in three reaction diffusion networks extensive asymptotic spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly a systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction diffusion networks for various boundary conditions the lyapunov dimension the sum of positive lyapunov exponents and the logarithm of the transient lifetime grow linearly with the system size the unstable manifold of the chaotic saddle has nearly the same dimension as the saddle itself and the stable manifold is nearly space filling

some properties of strong solutions to stochastic fuzzy differential equations we consider stochastic fuzzy differential equations driven by m dimensional brownian motion such equations can be useful in modeling of hybrid dynamic systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously under a boundedness condition which is weaker than linear growth condition and the lipschitz condition we obtain existence and uniqueness of solution to stochastic fuzzy differential equations solutions which are fuzzy stochastic processes and their uniqueness are considered to be in a strong sense an estimation of error of the picard approximate solution is established we give a boundedness type result for the solution defined on finite time interval also the stabilities of solution on initial condition and coefficients of the equation are shown the existence and uniqueness of a solution defined on infinite time interval is proven finally some applications of fuzzy stochastic differential equations are considered all the results presented in this paper apply to set valued stochastic differential equations

second type hukuhara differentiable solutions to the delay set valued differential equations abstract in this paper we consider the delay set valued differential equations with a recently introduced notion of a second type hukuhara derivative under condition that the right hand side of the equation is lipschitzian in the functional variable we obtain the existence and uniqueness of the solution to such the equations some properties of the solutions are established existence of at least one solution is also proved application of the second type hukuhara differentiability concept to the problems of set valued differential equations implies that the diameter of the solution values is a function nonincreasing in time

wavelike patterns in one dimensional coupled map lattices we investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two dimensional mapping the existence of such wavelike solutions is proved by the implicit function theorem with constraints we also examine the stabilities of these wave solutions under perturbations of uniform small deformation type we show that in some specific cases these perturbations are completely general the technique used in this paper is also applicable to investigate other space time regular patterns

the influence of noise on the logistic model the behavior of the logistic system which is generated by the functionf x ax 1 x changes in an interesting way if it is perturbed by external noise it turns out that the chaotic behavior which was predicted by li and yorke for orbits of period 3 becomes visible and that a sequence of mergence transitions occurs at the critical parameter the change of the invariant probability density and the lyapunov exponents are examined numerically the power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete time analog of a chapman kolmogorov equation

exactly solvable nonlinear model with two multiplicative gaussian colored noises abstract an overdamped system with a linear restoring force and two multiplicative colored noises is considered noise amplitudes depend on the system state x as x and x an exactly soluble model of a system is constructed due to consideration of a specific relation between noises exact expressions for the time dependent univariate probability distribution function and the fractional moments are derived their long time asymptotic behavior is investigated analytically it is shown that anomalous diffusion and stochastic localization of particles not subjected to a restoring force can occur

some results on sheaf solutions of sheaf set control problems abstract in this paper we study the existence and some properties of solutions of the so called set control differential equations scde and sheaf solutions of sheaf set control problems

approximate fokker planck equation of system driven by multiplicative colored noises with colored cross correlation abstract using the hanggi ansatz to truncate the evolution equation for probability density an approximate fokker planck equation afpe is derived this afpe is valid for one dimensional general systems driven by two multiplicative colored noises 1 0 and 2 0 that are correlated in color 3 0 under the condition for 1 2 and 3 to satisfy some inequalities we apply this afpe to a symmetrical bistable potential system driven by a colored multiplicative noise and a white additive noise with white cross correlation to verify the validity of our analytical approximation the numerical simulations for this system is performed we discovered a new phenomenon that the symmetry of stationary probability density broken by the correlation between the noises can be gradually recovered as the noise self correlation time is increased

phase ordering and persistence relative effects of space discretization chaos and anisotropy abstract the peculiar phase ordering properties of a lattice of coupled chaotic maps studied recently lemaitre chate phys rev lett 82 1999 1140 are revisited with the help of detailed investigations of interface motion it is shown that normal curvature driven like domain growth is recovered at larger scales than considered before and that the persistence exponent seems to be universal using generalized persistence spectra the properties of interface motion in this deterministic chaotic lattice system are found to interpolate between those of the two canonical reference systems the probabilistic ising model and the deterministic space continuous time dependent ginzburg landau equation

stability of wavelengths and spatiotemporal intermittency in coupled map lattices abstract in relation to spatiotemporal intermittency as it can be observed in coupled map lattices we study the stability of different wavelengths in competition introducing a two dimensional map we compare its dynamics with the one of the whole lattice we conclude that a good agreement between the two exists the reduced model also allows to introduce an order parameter which combines the diffusion parameter and the spatial wavelength under consideration

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

partition complexity in a network of chaotic elements a network of chaotic elements is investigated with the use of globally coupled maps elements can split into clusters with synchronized oscillation in a partially ordered phase the clustering has an inhomogeneous tree structure like replica symmetry breaking in spin glass the clustering has large variety by attractors and strongly depends on initial conditions the variety of clusterings is characterized by the distribution of partitions originated in spin glass theory the qualitative similarity and quantitative disagreement of the given attractors with a spin glass are clarified

quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series we describe methods of estimating the entire lyapunov spectrum of a spatially extended system from multivariate time series observations provided that the coupling in the system is short range the jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions this circumvents the curse of dimensionality that prevents the accurate reconstruction of high dimensional dynamics from observed time series the technique is illustrated using coupled map lattices as prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying

structure of complex periodic and chaotic media with spiral waves the spatiotemporal structure of reactive media supporting a solitary spiral wave is studied for systems where the local reaction law exhibits a period doubling cascade to chaos this structure is considerably more complex than that of simple period 1 oscillatory media as one moves from the core of the spiral wave the local dynamics takes the form of perturbed period doubled orbits whose character varies with spatial location relative to the core an important feature of these media is the existence of a curve where the local dynamics is effectively period 1 this curve arises as a consequence of the necessity to reconcile the conflict between the global topological organization of the medium induced by the presence of a spiral wave and the topological phase space structure of local orbits determined by the reaction rate law due to their general topological nature the phenomena described here should be observable in a broad class of systems with complex periodic behavior s1063 651x 96 12611 8

synchronization induced by periodic inputs in finite n unit bistable langevin models the augmented moment method we have studied the synchronization induced by periodic inputs applied to a finite n unit coupled bistable langevin model which is subjected to cross correlated additive and multiplicative noises the effects on the synchronization of the system size n the coupling strength and the cross correlation between additive and multiplicative noise have been investigated using the semi analytical augmented moment method amm which is a second order moment approximation for local and global variables h hasegawa phys rev e 67 2003 041903 a linear analysis of the stationary solution of the amm equations shows that the stability is improved degraded by positive negative couplings results of the nonlinear bistable langevin model are compared to those of the linear langevin model

predicting the future advantages of semilocal units in investigating gaussian radial basis function rbf networks for their ability to model nonlinear time series we have found that while rbf networks are much faster than standard sigmoid unit backpropagation for low dimensional problems their advantages diminish in high dimensional input spaces this is particularly troublesome if the input space contains irrelevant variables we suggest that this limitation is due to the localized nature of rbfs to gain the advantages of the highly nonlocal sigmoids and the speed advantages of rbfs we propose a particular class of semilocal activation functions that is a natural interpolation between these two families we present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks and very importantly are more accurate than rbf networks in the presence of irrelevant inputs on the mackey glass and coupled lattice map problems the speedup over sigmoid networks is so dramatic that the difference in training time between rbf and gaussian bar networks is minor gaussian bar architectures that superpose composed gaussians gaussians of gaussians to approximate the unknown function have the best performance we postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics which we call automatic connection pruning is an important factor in the success of this representation

pattern dynamics of a coupled map lattice for open flow abstract the pattern dynamics of the one way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich for medium and large coupling strengths we find spatially periodic quasiperiodic and chaotic patterns with temporal periodicity and analyze their stability with the help of a newly introduced spatial map criteria are established for predicting the down flow bifurcation behavior of the coupled map lattice and for selecting attractors through modulation of the boundary for smaller coupling strengths we find a novel regime in which chaotic defects form a periodic lattice that is shown to be the result of a boundary crisis

biholomorphic maps between teichmuller spaces in this paper we study biholomorphic maps between teichmuller spaces and the induced linear isometries between the corresponding tangent spaces the first main result in this paper is the following classification theorem if m and n are two riemann surfaces that are not of exceptional type and if there exists a biholomorphic map between the corresponding teichmuller spaces teich m and teich n then m and n are quasiconformally related also every such biholomorphic map is geometric in particular we have that every automorphism of the teichmuller space teich m must be geometric this result generalizes the previously known results see 2 5 7 and enables us to prove the well known conjecture that states that the group of automorphisms of teich m is isomorphic to the mapping class group of m whenever the surface m is not of exceptional type in order to prove the above results we develop a method for studying linear isometries between l 1 type spaces our focus is on studying linear isometries between banach spaces of integrable holomorphic quadratic differentials which are supported on riemann surfaces our main result in this direction theorem 1 1 states that if m and n are riemann surfaces of nonexceptional type then every linear isometry between a 1 m and a 1 n is geometric that is every such isometry is induced by a conformal map between m and n

relationship between bede gal differentiable set valued functions and their associated support functions in this study we adapt the concept of the bede gal derivative which was initially suggested for fuzzy number valued functions to set valued functions we use an example to demonstrate that this concept overcomes some of the shortcomings of the hukuhara derivative we prove some properties of bede gal differentiable set valued functions we also study the relationship between a bede gal differentiable set valued function and its value s support function which we call the associated support function we provide examples of set valued functions that are not bede gal differentiable whereas their associated support functions are differentiable we also present some applications of the bede gal derivative to solving set valued differential equations

colored noise enhanced stability in a tumor cell growth system under immune response in this paper we investigate a mathematical model for describing the growth of tumor cell under immune response which is driven by cross correlation between multiplicative and additive colored noises as well as the nonzero cross correlation in between the expression of the mean first passage time mfpt is obtained by virtue of the steepest descent approximation it is found i when the noises are negatively cross correlated 0 then the escape is slower than in the case with no correlation moreover in the case of positive cross correlation the escape time has a maximum for a certain intensity of one of the noises i e the maximum for mfpt identifies the noise enhanced stability of the cancer state ii the effect of the cross correlation time 3 on the mfpt is completely opposite for 0 and 0 iii the self correlation times 1 and 2 of colored noises can enhance stability of the cancer state while the immune rate can reduce it

stochastic resonance in an asymmetric bistable system with coloured noises and periodic rectangular signal abstract in this paper we consider the phenomenon of stochastic resonance sr in an asymmetric bistable system with coloured noises and periodic rectangular signal expression of the signal to noise ratio snr has been obtained under the adiabatic limit we investigate the effect of any system parameter such as p q r 1 2 on the snr the plot of snr 1 shows sr for some values of the additive noise self correlation time 2 but not for the whole range of 2 the system bias r suppresses the snr when the intensity of additive noise q is increased the sr phenomenon disappears in the plot of snr p but the plot of snr q presents sr for almost all values of the multiplicative noise intensity p

internal fluctuations period doubling and chemical chaos the effects of internal molecular fluctuations on period doubling bifurcations and chaotic band merging are studied in a well stirred reactive chemical system where spatial degrees of freedom play no role the calculations are carried out using a stochastic model based on reactive lattice gas cellular automata molecular fluctuations arising from reactive collisions are incorporated in the model and the mass action rate equations are recovered in the mean field limit large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes for the willamowski r ossler system the noise scaling exponent is consistent with that found for one dimensional quadratic maps subject to external noise the model provides a means to study small non equilibrium reacting systems where fluctuations may not be neglected

nonlinear variation of parameters formula for set differential equations in a metric space nonlinear variation of parameters formula for set differential equations in a metric space is developed investigating necessary tools such as differentiability of solutions relative to initial values other needed results are also proven

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

reactive lattice gas automata abstract a probabilistic lattice gas cellular automaton model of a chemically reacting system is constructed microdynamical equations for the evolution of the system are given the continuous and discrete boltzmann equations are developed and their reduction to a generalized reaction diffusion equation is discussed the microscopic reactive dynamics is consistent with any polynomial rate law up to the fourth order in the average particle density it is shown how several microscopic ca rules are consistent with a given rate law as most ca systems the present one has spurious properties whose effects are shown to be unimportant under appropriate conditions as an explicit example of the general formalism a ca dynamics is constructed for an autocatalytic reactive scheme known as the schlogl model simulations show that in spite of the simplicity of the underlying discrete dynamics the model exhibits the phase separation and wave propagation phenomena expected for this system because of the microscopic nature of the dynamics the role of internal fluctuations on the evolution process can be investigated

some unexpected consequences of the interaction between convective adjustment and horizontal diffusion abstract we consider the dynamics of a set of diffusively coupled grid points the dependent variable defined at each grid point is the salinity which is forced by a spatially uniform distribution of evaporation minus precipitation the nonlinearity in the system is a convective adjustment rule that sets the salinity back to zero if it ever exceeds one the aim of this study is to understand the spatial and temporal variability that results from the interaction between convective adjustment rules and horizontal diffusivity analytic results show that the model has a large number of different solutions which are periodic in space and time some of these solutions have a supprising structure in which convective adjustment is entirely suppressed at some grid points and occurs with a higher frequency at neighboring points numerical solutions indicate that these solutions have finite basins of attraction in the space of initial conditions thus small changes in the initial conditions can produce solutions with grossly different average properties numerical errors due to the finite size of the time step or roundoff can also have a decisive role in selecting the ultimate state which emerges from a particular condition for instance numerical errors can stabilize an unstable solution

on set differential equations in banach spaces a second type hukuhara differentiability approach in this paper we consider set differential equations in banach spaces and with the second type hukuhara derivative we show that a sequence of successive approximations converges uniformly to a unique local solution of a cauchy problem some comparison results are formulated and a continuity of solution with respect to equation data is shown the existence of a global solution is also established

multiscaling of the graph length in coupled map lattices we consider generalized scaling exponents for the graph of a scalar function to allow for multiscaling of the graph length these generalized exponents are related to the moments of the distribution of roughness over the support of the graph we report numerical computations of these exponents for the graphs of coupled map lattices exhibiting phase transitions between laminar and turbulent behaviour we observe multiscaling of the graph in the transition region furthermore the generalized dimensions d q are computed for a conserved measure of graph roughness

chaotic traveling waves in a coupled map lattice traveling waves triggered by a phase slip are studied in a coupled map lattice a local phase slip affects globally the system which is in strong contrast with kink propagation attractors with different velocities coexist and form quantized bands determined by the number of phase slips if the system size is not far from an integer multiple of the selected wavelength attractors are tori otherwise weak chaos induces modulation of waves or a chaotic itinerancy of traveling states with a long ranged temporal correlation supertransients before the formation of traveling waves are noted in the high nonlinearity regime in the weaker nonlinearity there are fluctuations of domain sizes and brownian like motion of domains propagation of chaotic domains by phase slips is also found

stochastic time delayed systems driven by correlated noises steady state analysis abstract in the present paper a class of stochastic time delayed systems driven by correlated gaussian white noises are considered novikov s theorem is used to derive delay fokker planck equations in the case of small time delays approximate stationary solutions are obtained as a special case the delay fokker planck equation and the approximate stationary probability density function is obtained for a bistable system numerical simulations show that the small delay approximation is a good approximation in the case of small delay furthermore the effects of the correlated noises and the feedback are investigated the critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by the degree of the correlation of the noises and e the strength of the feedback both and e can change the curve of the stationary probability density function from a bimodal to a unimodal structure

an exactly solvable nonlinear model constructive effects of correlations between gaussian noises abstract a system with two correlated gaussian white noises is analysed this system can describe both stochastic localization and long tails in the stationary distribution correlations between the noises can lead to a nonmonotonic behaviour of the variance as function of the intensity of one of the noises and to a stochastic resonance a method for improving the transmission of external periodic signal by tuning parameters of the system discussed in this paper is proposed

stability criteria for set control differential equations abstract the existence and comparison results on solutions of set control differential equation were studied in n d phu t t tung some results on sheaf solutions of sheaf set control problems nonlinear analysis 67 2007 1309 1315 in this paper we present the stability criteria for solutions of set control differential equation

mode locking in coupled map lattices abstract we study propagation of pulses along one way coupled map lattices which originate from the transition between two superstable states of the local map the velocity of the pulses exhibits a staircase like behaviour as the coupling parameter is varied for a piecewise linear local map we prove that the velocity of the wave has a devil s staircase dependence on the coupling parameter a wave travelling with rational velocity is found to be stable to parametric perturbations in a manner akin to rational mode locking for circle maps we provide evidence that mode locking is also present for a broader range of maps and couplings

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

intrinsic fluctuations in chaotic dynamics abstract the multivariate master equation of a chemical system exhibiting spatio temporal chaos is investigated it is shown that the probability distribution in the presence of fluctuations remains centered on the underlying deterministic attractor

cross correlation enhanced stability in a tumor cell growth model with immune surveillance driven by cross correlated noises the transient properties of a tumor cell growth model with immune surveillance driven by cross correlated multiplicative and additive noises are investigated the explicit expression of extinction rate from the state of a stable tumor to the state of extinction is obtained based on the numerical computations we find the following i the intensity of multiplicative noise d and the intensity of additive noise enhance the extinction rate for the case of 0 i e denotes cross correlation intensity between two noises but for the case of 0 a critical noise intensity d or exists at which the extinction rate is the smallest d and at first weaken the extinction rate and then enhance it ii the immune rate and the cross correlation intensity play opposite roles on the extinction rate i e enhances the extinction rate of the tumor cell while weakens the extinction rate of the tumor cell namely the immune rate can enhance the extinction of the tumor cell and the cross correlation between two noises can enhance stability of the cancer state

renormalization group for strongly coupled maps systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos we show how the well known renormalization group rg of unimodal maps can be extended to the coupled systems and in particular to coupled map lattices cmls with local diffusive coupling the rg relation derived for cmls is nonperturbative i e not restricted to a particular class of configurations nor to some vanishingly small region of parameter space after defining the strong coupling limit in which the rg applies to almost all asymptotic solutions we first present the simple case of coupled tent maps we then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties extending the formal approach developed by collet and eckmann for single maps we finally discuss and illustrate the general consequences of the rg cmls are shown to share universal properties in the space continuous limit which emerges naturally as the group is iterated we prove that the scaling properly ties of the local map carry to the coupled systems with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems this explains various scaling laws and self similar features previously observed numerically

set valued and fuzzy stochastic differential equations driven by semimartingales abstract in the paper we present set valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties then we study the existence of solutions to set valued and fuzzy set valued stochastic differential equations driven by semimartingales the stability of solutions is also established

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

stability of set differential equations and applications abstract the paper introduces some results on stability of sheaf solutions exponential stability of solutions and sheaf solutions of set differential equations and their applications to set control differential equations

the initial value problem for interval valued second order differential equations under generalized h differentiability in this paper the interval valued second order differential equations under generalized hukuhara differentiability isdes are introduced under suitable conditions we obtain the existence and uniqueness results of solutions to isdes to prove this assertion we use idea of contraction principle and successive approximations furthermore we use the method based on properties of linear transformations ltm to find the explicit solution of initial value problem for linear second order differential equation with interval valued forcing function and with interval initial values iivp we apply the linear transformations method to two example problems including a vibrating mass and an electrical circuit finally the method based on the analysis of a solution to real valued second order differential equation is investigated to solve interval valued second order differential equations with interval valued coefficients interval valued forcing function and interval initial values some examples are presented to illustrate applicability of the proposed method

competitively coupled maps and spatial pattern formation spatial pattern formation is a key feature of many natural systems in physics chemistry and biology the essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo spontaneous symmetry breaking leading to a stable spatial pattern this problem is most commonly studied using partial differential equations to model a reaction diffusion system of the type introduced by turing we report here on a much simpler and more robust model of spatial pattern formation which is formulated as a novel type of coupled map lattice in our model the local site dynamics are coupled through a competitive rather than diffusive interaction depending only on the strength of the interaction this competitive coupling results in spontaneous symmetry breaking of a homogeneous initial configuration and the formation of stable spatial patterns this mechanism is very robust and produces stable pattern formation for a wide variety of spatial geometries even when the local site dynamics is trivial

complex spatiotemporal patterns in two lattice models with instability abstract in this paper we consider two lattice models i the discretized version of a simple nonlinear partial differential equation pde with a singular term and ii a coupled map lattice cml with unstable coupling both systems are defined by simple iteration rules involving the nearest neighbour grid points of the corresponding one dimensional lattice we show numerically that these models result in an apparently stochastic spatiotemporal behaviour and exhibit interesting regimes as the function of the parameters of the models in particular we find that by varying the relative weight b of the singular term in the pde the total width of the solution scales with b the cml leads to an intermittent behaviour between structured and turbulent regimes

effect of correlated dichotomous noises on stochastic resonance in a linear system a linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case the exact expressions of output signal amplitude and signal to noise ratio snr of the system were derived by means of numerical calculations we found that i at some fixed multiplicative noise intensities the output signal amplitude with frequency exhibits the structure of a weak peak even no peak as the dichotomous noise is asymmetric ii in the case of asymmetric dichotomous noise the signal frequency can cause non monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity iii the curve of snr with frequency has a weak peak and a trough in the case of symmetric dichotomous noise but no peak with asymmetric iv whether the multiplicative noise is symmetric or asymmetric the noise can enhance response of the system v the snr increases with the correlation strength between the two noises decreasing in addition the plane of multiplicative noise intensity versus noise symmetric parameter was plotted

dynamical properties of a logistic growth model with cross correlated noises abstract a logistic growth model driven by additive and multiplicative noises which are correlated with each other is investigated using the novikov theorem and the projection operator method we obtain the analytic expressions of the stationary probability distribution p s t x the relaxation time t c and the normalized correlation function c s of this system the computational results show that the relaxation time t c increases as the cross correlated time increases but decreases while the cross correlated strength increases the relationship between the relaxation time c s and the decay time s is given correlation time and correlation strength play an opposite role on dynamic properties in this logistic growth model

on asymptotic teichmuller space in this article we prove that for any hyperbolic riemann surface m of infinite analytic type the little bers space q0 m is isomorphic to c0 as a consequence of this result if m is such a riemann surface then its asymptotic teichm uller space at m is bi lipschitz equivalent to a bounded open subset of the banach space l c0 further if m and n are two such riemann surfaces their asymptotic teichm uller spaces at m and at n are locally bi lipschitz equivalent

universality and scaling of period doubling bifurcations in a dissipative distributed medium abstract a homogeneous medium consisting of nonlinear elements demonstrating transition to chaos via period doubling bifurcations is considered the coupling between the elements is supposed to be of a dissipative type i e it tends to equalize their instantaneous states using the renormalization group approach the following scaling law for weakly inhomogeneous states near the critical point is obtained at each period doubling the spatial scale increases by 2 on the basis of this law the scaling hypotheses for the transition to chaos in the semi infinite and finite systems are proposed the scaling properties are verified by the numerical calculations with a simple model

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model

set differential equations versus fuzzy differential equations the study of fuzzy differential equations fdes forms a suitable setting for a mathematical modeling of real world problems in which uncertainties or vagueness pervades in recent years the theory of fdes has been investigated extensively in the original formulation as well as in an alternative framework which leads to ordinary multivalued differential inclusions it has recently been realized that initiating the study of set differential equations in a metric space has several advantages in addition to providing a natural setting for considering fdes in this paper we present some interesting results in this direction with the necessary background material