spatiotemporal complexity of the cubic quintic nonlinear schrodinger equation the integrability of the cubic quintic nonlinear schrodinger equation is investigated numerically by analytically studying the linear stability of the homogeneous state and numerically solving such a continuum hamiltonian dynamic system the authors show that the quintic nonlinear term leads to a spatiotemporal complexity of wave fields and illustrate that this behaviour is associated with the stochastic partition of energy in fourier modes in addition they show the presence of the stochastic motion is due to the homoclinic orbit crossings

markov chains of nonlinear markov processes and an application to a winner takes all model for social conformity we discuss nonlinear markov processes defined on discrete time points and discrete state spaces using markov chains in this context special attention is paid to the distinction between linear and nonlinear markov processes we illustrate that the chapman kolmogorov equation holds for nonlinear markov processes by a winner takes all model for social conformity

entrainment control in a noisy neural system the open plus closed loop opcl entrainment control put forth by jackson and grosu physica d 85 1995 is applied to an effective neuron system as a way to extract stable limit cycles from a chaotic attractor analogous to the retrieval of memories from a memory searching state additive gaussian white noise representing the natural noise inherent in any real dynamical system is added to the entrainment control mechanism moderate levels of additive noise have little effect on successful entrainment as reflected in phase space plots and lyapunov exponents all three lyapunov exponents are negative which suggests parallels between opcl control and chaotic synchronization al 2

a modified interpolated cell mapping method abstract a modified interpolated cell mapping micm method is developed for global analysis of deterministic dynamical systems with smooth basin boundaries by improving the algorithm of the interpolated cell mapping icm and including the idea of sampling mappings of cells from the generalized cell mapping gcm micm gives a more complete and precise global analysis of systems that icm in addition based on analysis using micm a method using exact mappings is proposed to remedy the inaccuracy and incompleteness of global analysis due to interpolated mappings and the assumption of the sink cell for the three systems studied in this paper this method locates identical attractors and basins of attraction as the integration of a grid of points igp method with a 100 fold improvement in computational efficiency

a procedure for obtaining general nonlinear fokker planck equations abstract a procedure for deriving general nonlinear fokker planck equations fpes directly from the master equation is presented the nonlinear effects are introduced in the transition probabilities which present a dependence on the probabilities for finding the system in a given state it is shown that the fpes obtained from master equations describing transitions among discrete and continuous sets of states are identical within such a procedure we construct nonlinear fpes that appear to be very general our general fpes recover as particular cases nonlinear fpes investigated previously by many authors introduced on a purely phenomenological basis and they lead to the possibility of more complete and complex diffusive equations

computational chaos a prelude to computational instability abstract chaotic behavior sometimes occurs when difference equations used as approximations to ordinary differential equations are solved numerically with an excessively large time increment in two simple examples we find that as increases chaos first sets in when attractor a acquires two distinct points that map to the same point this happens when a acquires slopes of the same sign in a rectifying coordinate system at two consecutive intersections with the critical curve chaotic and quasi periodic behavior may then alternate within a range of before computational instability finally prevails bifurcations to and from chaos and transitions to computational instability are highly scheme dependent even among differencing schemes of the same order systems exhibiting computational chaos can serve as illustrative examples in more general studies of noninvertible mappings

non linear vibration analysis of multilayer beams by incremental finite elements part i theory and numerical formulation an incremental variational equation for non linear motions of multilayer beams composed of n stiff layers and n 1 soft cores is derived from the dynamic virtual work equation by an appropriate integration procedure the kinematical hypotheses of eulerbernoulli and timoshenko beam theories are used to describe the displacement fields of the stiff layers and cores respectively an efficient solution procedure of incremental harmonic balance method type with use of finite elements is developed to demonstrate its capability some problems in free non linear vibrations of multilayer beams are treated by using the procedure results are compared with those available in the literature the effects of damping are also included in this investigation but are described in part ii 1 of this paper in which a number of undamped and damped forced non linear vibration problems are studied results in the form of tables and plots are also presented and comparisons are made with those available in the literature

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

application of the incremental harmonic balance method to cubic non linearity systems abstract in this paper the formulation of the incremental harmonic balance ihb method is derived for a general system of differential equations with cubic non linearity which governs a wide range of engineering problems such as large amplitude vibration of beams or plates an incremental arc length method combined with a cubic extrapolation technique is adopted to trace the response curve automatically the stability of its periodic solutions can also be evaluated from the ihb formulation by multi variable floquet theory hsu s method is adopted for computing the transition matrix at the end of one period two numerical examples are presented which demonstrate the effectiveness of the ihb method and hsu s method in treating the non linear vibration of a strongly non linear multiple degree of freedom system

non linear dynamic analysis and control of chaos for a two degrees of freedom rigid body with vibrating support abstract the dynamic behaviors of a two degrees of freedom rigid body with vibrating support are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using the lyapunov direct method the conditions of stability of the relative equilibrium position can be determined the incremental harmonic balance method ihb is used to find the stable and unstable periodic solutions for the strongly non linear system by applying various numerical results such as phase plane poincare map time history and power spectrum analysis a variety of periodic solutions and the phenomena of the chaotic motion is presented the effects of the changes of parameters in the system can be found in the bifurcation diagrams further the chaotic behavior is verified by using lyapunov exponents the modified interpolated cell mapping method micm is used to study the basins of attraction of periodic attractors and the fractal structure besides additions of a constant torque a periodic torque addition of dither signals delayed feedback control adaptive control and bang bang control are used to control the chaos phenomena effectively

nonlinear markov semigroups and interacting levy type processes semigroups of positivity preserving linear operators on measures of a measurable space x describe the evolutions of probability distributions of markov processes on x their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions b x on x describe the evolutions of averages over the trajectories of these markov processes in this paper we introduce and study the general class of semigroups of non linear positivity preserving transformations on measures that is non linear markov or feller semigroups an explicit structure of generators of such groups is given in case when x is the euclidean space r d or more generally a manifold showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for markov models of interacting particles well posedness results for these equations are given together with applications to interacting particles dynamic law of large numbers and central limit theorem the latter being new already for the standard coagulation fragmentation models

the response of two degree of freedom systems with quadratic non linearities to a combination parametric resonance abstract the response of two degree of freedom systems with quadratic non linearities to a combination parametric resonance in the presence of two to one internal resonances is investigated the method of multiple scales is used to construct a first order uniform expansion yielding four first order non linear ordinary differential equations governing the modulation of the amplitudes and the phases of the two modes steady state responses and their stability are computed for selected values of the system parameters the effects of detuning the internal resonance detuning the parametric resonance the phase and magnitude of the second mode parametric excitation and the initial conditions are investigated the first order perturbation solution predicts qualitatively the trivial and non trivial stable steady state solutions and illustrates both the quenching and saturation phenomena in addition to the steady state solutions other periodic solutions are predicted by the perturbation amplitude and phase modulation equations these equations predict a transition from constant steady state non trivial responses to limit cycle responses hopf bifurcation some limit cycles are also shown to experience period doubling bifurcations the perturbation solutions are verified by numerically integrating the governing differential equations

macroscopic limit cycle via pure noise induced phase transitions bistability generated via a pure noise induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics it allows an analytical study of the phase diagram in more general cases than previous methods in addition using this approach we investigate spatially extended systems with two degrees of freedom per site for this system the analytic solution of the stationary fokker planck equation is not available and a standard mean field approach cannot be used to find noise induced phase transitions a different approach based on cumulant dynamics predicts a noise induced phase transition through a hopf bifurcation leading to a macroscopic limit cycle motion which is confirmed by numerical simulation

logarithmic diffusion and porous media equations a unified description in this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear fokker planck equation in its diffusive term goes to zero a linear drift and a source term are considered in this equation its solution has a lorentzian form consequently this equation characterizes a superdiffusion like a levy kind in addition an equation that unifies the porous media and the logarithmic diffusion equations including a generalized diffusion equation in fractal dimension is obtained this unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes

two distinct mechanisms of coherence in randomly perturbed dynamical systems we carefully examine two mechanisms coherence resonance and self induced stochastic resonance by which small random perturbations of excitable systems with large time scale separation may lead to the emergence of new coherent behaviors in the form of limit cycles we analyze what controls the degree of coherence in these two mechanisms and classify their very different properties in particular we show that coherence resonance arises only at the onset of bifurcation and is rather insensitive against variations in the noise amplitude and the time scale separation ratio in contrast self induced stochastic resonance may arise away from bifurcations and the properties of the limit cycle it induces are controlled by both the noise amplitude and the time scale separation ratio

a novel higher order sliding mode control scheme a higher order sliding mode control algorithm is proposed for a class of uncertain multi input multi output nonlinear systems this problem can be viewed as the flnite time stabilization of a higher order input output dynamic system with bounded uncertainties the developed control scheme is based on geometric homogeneity and sliding mode control the proposed procedure provides explicit conditions on the controller parameters and guarantees robustness against uncertainties an illustrative example of a hovercraft vessel control demonstrates the advantages of the strategy

period doubling bifurcations chaos phase locking and devil s staircase in a bonhoeffer van der pol oscillator abstract the effect of a periodic input current a 1 cos t in the bonhoeffer van der pol oscillator along with a bias a 0 is investigated numerically as the parameter a 1 is varied in the absence of bias by holding the other parameters at constant values typical period doubling bifurcation sequence is found to occur leading to chaotic motion in agreement with the feigenbaum scenario when the bias is switched on at the transition to chaos frequency locking is observed in the system the frequency locked intervals exhibit complete devil s staircase similar to the one observed in belousov zhabotinsky reaction

sliding mode control in discrete state and hybrid systems the sliding mode control approach is developed for a class of discrete state systems in a metric space a concept of trajectory continuity is introduced which allows the use of sliding mode design techniques similar to that in continuous state systems this approach is then applied to a class of hybrid systems which consists of a continuous plant an interface and a discrete state controller the introduction of the sliding mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem

chaos from nonlinear markov processes why the whole is different from the sum of its parts abstract nonlinear markov processes have been frequently used to address bifurcations and multistability in equilibrium and non equilibrium many body systems however our understanding of the range of phenomena produced by nonlinear markov processes is still in its infancy we demonstrate that in addition to bifurcations and multistability nonlinear markov processes can exhibit another key phenomena well known in the realm of nonlinear physics chaos it is argued that chaotically evolving process probabilities are a generic feature of many body systems exhibiting nonlinear markov processes even if the isolated subsystems do not exhibit chaos that is when considering a nonlinear markov process as an entity of its own type then the nonlinear markov process in general is qualitatively different from its constituent subprocesses which reflects that the many body system as a whole is different from the sum of its parts

stability analysis of mean field type nonlinear fokker planck equations associated with a generalized entropy and its application to the self gravitating system multidimensional nonlinear fokker planck equations of mean field type are proposed within the framework of generalized thermostatistics to develop a general formulation of stability analysis of their solutions two types of eigenvalue equations are studied the nonlinear fokker planck equations are shown to exhibit an h theorem with a liapunov functional that takes the form of a free energy involving generalized entropies of tsallis the second order variation of the liapunov functional is computed to conduct local stability analysis and the associated eigenvalue equation is derived for an arbitrary form of mean field coupling potential assuming quasiequilibrium for the velocity distribution the reduced eigenvalue equation with space coordinates alone is also obtained the alternative type of eigenvalue equation based on the linearization of the nonlinear fokker planck equations is presented taking the mean field coupling potential to be the gravitational one the nonlinear fokker planck equation in terms of three dimensional velocity and space coordinates together with the framework of stability analysis is shown to be applicable to a mean field model of self gravitating system by solving the eigenvalue equation for the eigenfunction with 0 eigenvalue the occurrence of stability change of the equilibrium probability density with spherical symmetry is discussed

nonequilibrium wetting transitions with short range forces we analyze within mean field theory as well as numerically a kardar parisi zhang equation that describes nonequilibrium wetting both complete and critical wettitng transitions were found and characterized in detail for one dimensional substrates the critical weting temperature is depressed by fluctuations in addition we have investigated a region in the space of parameters temperature and chemical potential where the wet and nonwet phases coexist finite size scaling analysis of the interfacial detaching times indicates that the finite coexistence region survives in the thermodynamic limit within this region we have observed stable or very long lived structures related to spatiotemporal intermittency in other systems in the interfacial representation these structures exhibit perfect triangular pyramidal patterns in one dimension two dimensions which are characterized by their slope and size distribution

stochastic feedback nonlinear families of markov processes and nonlinear fokker planck equations abstract we discuss two fundamental aspects of fokker planck equations that are nonlinear with respect to probability densities first we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions second we demonstrate that nonlinear fokker planck equations can be interpreted as linear fokker planck equations describing nonlinear families of markov diffusion processes we exploit this finding in order to derive complete hierarchies of probability densities from nonlinear fokker planck equations

the response of two degree of freedom systems with quadratic non linearities to a parametric excitation the method of multiple scales is used to analyze the response of two degree of freedom systems with quadratic non linearities to a parametric harmonic excitation having the frequency four ordinary differential equations are derived to describe the modulation of the amplitudes and the phases when 2 2 1 and either 2 1 or 2 2 where 1 and 2 are the linear undamped natural frequencies of the system two critical values 1 and 2 of the amplitude f of the excitation are identified in the analysis when f 2 the amplitude of the directly excited mode grows exponentially with time according to the linear analysis whereas the amplitudes of both modes achieve steady state constant values irrespective of the initial amplitudes according to the non linear analysis when f 1 the motion decays to zero according to both the linear and non linear analyses when 1 f 2 the motion decays to zero according to the linear analysis whereas it achieves a periodic steady state or decays to zero depending on the initial amplitudes according to the non linear analysis this is an example of subcritical instability when 2 2 the steady state value of the higher mode which is directly excited is a constant that is independent of the excitation of amplitude f whereas the amplitude of the lower mode which is indirectly excited through internal resonance grows with the excitation amplitude f this is another example of saturation

chaos control of new mathieu van der pol systems with new mathieu duffing systems as functional system by gyc partial region stability theory abstract in this paper a new strategy by using gyc partial region stability theory is proposed to achieve chaos control using the gyc partial region stability theory the new lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error numerical simulations are given for new mathieu van der pol system and new mathieu duffing system to show the effectiveness of this strategy

output tracking control of uncertain nonlinear second order systems abstract the solution of a tracking problem for a secondorder nonlinear system with uncertain dynamics and incomplete state measurement is obtained by means of a procedure directly inspired by the solution of the classical minimum time optimal control problem two different types of uncertainty are considered in the paper in the first case a constant bound on the uncertain dynamics is assumed to be known in the second case the bound is a function of both the measurable and the unmeasurable state variable of the system in both cases the possibility of applying the proposed control algorithms is proved to be determined by a proper choice of the control signal features the resulting system is characterized by a suitable feedback switching logic and the convergence of the system trajectory to the desired one or to a vicinity of this latter is proved also in the uncertain case

discrete variable structure integral controllers the subject of this paper is the analysis and the design of a class of robust discrete time variable structure controllers of integral type we refer to the discontinuous integral control dic technique already developed by the authors for the time continuous case where a nonlinear integral action is used for estimating the external disturbance and keeping small the discontinuous term in the control law and the subsequent chattering effect a discretised version of the dic algorithm which is properly modified in order to take into account the time derivative information on the controlled variable is introduced and discussed the so obtained discrete time controller shows to be very effective in reducing the chattering when the system parameters are known moreover to cope with a specific case of unknown parameters a new adaptive control structure is proposed and analysed the local asymptotic stability of the resulting closed loop system is proved in the case of constant external disturbances finally simulation results on the velocity control of a dc motor end the paper

bifurcation and chaotic motion of a soliton in a long josephson junction oscillator the fluxon dynamics of a long josephson junction ljj is investigated numerically the effect of the surface resistance of the superconductor on the bifurcation phenomenon is examined in detail we show the occurrence of a period doubling route to chaos and the reappearance of low order periodic motions in the ljj by varying the magnitude of the external force the chaotic attractors of the ljj are characterized using maximal lyapunov exponents and a fractal correlation dimension we show the existence of noise induced oscillations in a force free ljj system finally the influence of noise on the periodic and chaotic dynamics is also presented

adaptive control in nonlinear dynamics abstract we extend an adaptive control algorithm recently suggested by huberman and lumer to multi parameter and higher dimensional nonlinear systems this control mechanism is remarkably effective in returning a system to its original dynamics after a sudden perturbation in the system parameters changes the dynamical behaviour we find that in all cases the recovery time is linearly proportional to the inverse of control stiffness for small stiffness in higher dimensions there is an additional optimization problem since increasing stiffness beyond a certain value can retard recovery the control of fixed point dynamics in systems capable of a wide variety of dynamical behaviour is demonstrated we further suggest methods by which periodic motion such as limit cycles can be adaptively controlled and demonstrate the robustness of the procedure in the presence of additive background noise

horseshoes in the driven damped pendulum abstract folding and horseshoes are found in two dimensional maps computed from simulations of the driven damped pendulum a simple model illustrates how horseshoes produce fractal boundaries of the basins of attraction for separate steady state solutions fractal basin boundaries result in noise amplification through extrinsic intermittency and in long transients when the dimension of the boundary approaches that of the phase space folding of the phase space beyond a crisis in which chaotic attractors collide with the boundary that separates their basins of attraction produces complex intermittent dynamical behavior both noise and crisis induced intermittency can produce power spectra s 1 with 1 over several decades in frequency

dynamical mean field theory of spiking neuron ensembles response to a single spike with independent noises a semianalytical dynamical mean field theory has been developed for a study of dynamics of an ensemble of n unit fitzhugh nagumo neurons subject to white noises assuming weak noises and the gaussian distribution of state variables we have driven equations of motions for moments of local and global variables dynamical mean field approximation dma has replaced original 2n dimensional stochastic differential equations des by eight dimensional deterministic des whereas the conventional moment method yields n 2n 3 dimensional deterministic des for local variables we have discussed the dependence of the spike firing precision and the synchronization on the noise intensity synaptic coupling and the size of the neuron ensemble the spike timing precision is shown to be improved by increasing the size of the neuron ensemble even when there are no couplings among neurons when the coupling is introduced neurons in ensembles respond to an input spike with a partial synchronization results calculated by our dma theory are in good agreement with those obtained by direct simulations dma theory is extended to a large cluster which can be divided into multiple subclusters according to their functions a model calculation has demonstrated that when the noise intensity is moderate the spike propagation with a fairly precise timing is possible among noisy subclusters with feed forward couplings as in the synfire chain we have compared dma theory with the conventional moment method showing that the former may be alternatively derived from the latter by a reduction in the number of moments with the mean field approximation

field theory of critical behavior in a driven diffusive system we use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field a fixed point stable belowd c 5 is found to govern the critical behavior scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in 5 d spatial correlations are found to be very anisotropic with elongated correlations along the external field long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents

regular and chaotic dynamic analysis and control of chaos of an elliptical pendulum on a vibrating basement the dynamic behavior of an elliptical pendulum subjected to external disturbance is studied in this paper the lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system by applying numerical results phase diagrams power spectrum period t maps and lyapunov exponents are presented to observe periodic and chaotic motions the effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams for global analysis the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping micm method finally several methods the delayed feedback control the addition of constant torque the addition of periodic force adaptive control algorithm and bang bang control are used to control chaos effectively

periodic forced vibration of unsymmetrical piecewise linear systems by incremental harmonic balance method abstract a single degree of freedom non linear system subjected to periodic excitation is considered the non linearity is in the restoring force and is represented by unsymmetrical piecewise linear stiffness the steady state response are analysed by an extended incremental harmonic balance ihb method all possible subharmonic harmonic and superharmonic resonances and bifurcations are sought the results reveal some interesting details of responses of unsymmetrical piecewise linear systems comparisons with available published findings are also made

effects of phase space discretization on the long time behavior of dynamical systems abstract we investigate the effects that roundoff errors have on discrete time dynamical systems computer generated orbits terminate in loops whose lengths scale with the machine precision in a universal way we present arguments to explain this fact

bifurcations and chaos of the bonhoeffer van der pol model periodic and chaotic behaviour of the bonhoeffer van der pol model of a nerve membrane driven by a periodic stimulating current a1 cos omega t is investigated results show that there exist ordinary and reversed period doubling cascades and a mode locking state at low driving amplitudes a1 there are period doubling and chaotic states but no impulse solutions when a1 is larger than a0 0 749 there are chaotic reversed period doubling and mode locking states and there also exist impulse trains a mode locking state with period 4 over a very large range of amplitudes is also found at a1 1 7059 the system goes back to a one period state

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

integral kinetic method for one dimension the spherical case the integral method to numerically calculate the time evolution of kinetic systems is discussed and improved for one dimensional problems the new approach is applied to the solution of the spherically symmetric one component plasma kinetic evolution the results are compared with those obtained by means of the finite difference solution to the equivalent fokker planck kinetic equation

evolution of a stochastic system within the framework of tsallis statistics abstract the general approach of a nonlinear fokker planck equation is applied to investigate the behavior of main statistical moments of a stochastic system it was shown that the system described by tsallis statistics can undergo transitions inherent to multiplicative noise induced transitions the scaling laws of motion are defined to identify an anomalous time behavior of the system with multiplicative noise

the minimal center of attraction of measurable systems and their discretizations a generalization of the birkhoff minimal center of attraction is introduced and investigated for dynamical systems generated by single and multi valued borel measurable mappings in particular it is shown to be equal to the minimal closed set containing the supports of the semi invariant measures of the system its approximation under the spatial discretization of the state space is also considered

phase separation dynamics in driven diffusive systems we study phase separation dynamics in a driven diffusive system our simulations are based on the cahn hilliard equation with an additional flux term due to an external field we study the dynamical scaling parallel and perpendicular to the field a crossover is observed from isotropic domains at early times to extremely anisotropic domains at later times we find that the inverse interfacial density an isotropic measure of the domain size increases ast with 1 3 from early times independent of the field strength even though we do not observe dynamical scaling during these times our results indicate that a growth exponent 1 3 may be more universal than previously expected we analyze the dynamics in terms of surface driven instabilities and one dimensional solitary waves

pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control a new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable i e these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values it is called pragmatical generalized synchronization finally two numerical examples are studied for two quantum cnn oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double duffing chaotic system as a goal system

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

chaos chaos control and synchronization of a gyrostat system abstract the dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper by applying numerical results phase diagrams power spectrum period t maps and lyapunov exponents are presented to observe periodic and choatic motions the effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams for global analysis the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping micm method several methods the delayed feedback control the addition of constant torque the addition of periodic force the addition of periodic impulse torque injection of dither signal control adaptive control algorithm aca control and bang bang control are used to control chaos effectively finally synchronization of chaos in the gyrostat system is studied

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

brief paper sliding mode boundary control of a parabolic pde system with parameter variations and boundary uncertainties this paper considers the stabilization problem of a one dimensional unstable heat conduction system rod modeled by a parabolic partial differential equation pde powered with a dirichlet type actuator from one of the boundaries by applying the volterra integral transformation a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties the associated lyapunov function is used for designing an infinite dimensional sliding manifold on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances it is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero a continuous control law satisfying the reaching condition is obtained by passing a discontinuous signum signal through an integrator

slow periodic motions with internal sliding modes in variable structure systems singularly perturbed relay systems sprs in which the reduced systems have the stable periodic motions with internal sliding modes are studied the slow motion integral manifold of such systems consists of the parts which correspond to the different values of relay control and the solutions may contain the jumps from one part of the slow manifold to another for such systems a theorem about existence and stability of the periodic solutions is proved an algorithm of asymptotic representation for this periodic solutions using boundary layer method is presented it is proved that in the neighbourhood of the break away point the asymptotic representation starts with the first order boundary layer function

on the linear discrepancy model and risky shifts in group behavior a nonlinear fokker planck perspective using a nonlinear fokker planck perspective we re formulate the linear discrepancy model proposed by boster and colleagues that describes the emergence of risky shifts during group decision making analytical expressions for the stationary case are derived and risky shifts are obtained by monte carlo simulations striking similarities with the kuramoto model for group synchronization are pointed out

consequences of the h theorem from nonlinear fokker planck equations a general type of nonlinear fokker planck equation is derived directly from a master equation by introducing generalized transition rates the h theorem is demonstrated for systems that follow those classes of nonlinear fokker planck equations in the presence of an external potential for that a relation involving terms of fokker planck equations and general entropic forms is proposed it is shown that at equilibrium this relation is equivalent to the maximum entropy principle families of fokker planck equations may be related to a single type of entropy and so the correspondence between well known entropic forms and their associated fokker planck equations is explored it is shown that the boltzmann gibbs entropy apart from its connection with the standard linear fokker planck equation may be also related to a family of nonlinear fokker planck equations

application of stochastic control techniques to chaotic nonlinear systems a control algorithm based on stochastic control techniques is devised for chaotic nonlinear systems the algorithm uses a state estimator based on the kalman filter and yields performance improvements in at least some regions of state space with respect to that obtainable by use of a controller utilizing only the conditional mean of the system state vector the method is applied to two typical chaotic nonlinear systems the henon heiles system and the lorenz system and their behavior with control is explored numerically

sliding mode control in dynamic systems the concept of sliding modes in abstract dynamic systems described by a semigroup of state space transformations is introduced the sliding mode design procedure is used for designing finite observers sliding mode control for systems with delays and differential difference systems which is illustrated by sliding mode control of longitudinal oscillations

reentrant transition induced by multiplicative noise in the time dependent ginzburg landau model an effect of multiplicative noise in the time dependent ginzburg landau model is reported namely that noise at a relatively low intensity induces a phase transition towards an ordered state whereas strong noise plays a destructive role driving the system back to its disordered state through a reentrant phase transition the phase diagram is calculated analytically using a mean field theory and a more sophisticated approach and is compared with the results from extensive numerical simulations

noise induced escape from attractors the author deals with several aspects of kautz 1987 1988 minimum principle for the noise induced escape from attractors he presents a slightly simpler derivation points out a connection with lyapunov exponents and invariant manifolds and generalises to chaotic maps

non linear kinetics underlying generalized statistics abstract the purpose of the present effort is threefold firstly it is shown that there exists a principle that we call kinetical interaction principle kip underlying the non linear kinetics in particle systems independently on the picture kramers boltzmann used to describe their time evolution secondly the kip imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy thirdly the kip allows on one hand to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and on the other hand suggests how we can introduce naturally new distributions finally as a working example of the approach to the non linear kinetics here presented a new non extensive statistics is constructed and studied starting from a one parameter deformation of the exponential function holding the relation f x f x 1

noise induced jumps in two coupled duffing oscillators abstract we consider two coupled duffing oscillators with the coexistence of four attractors switching between the coexisting attractors by noises is investigated three types of noises such as gaussian amplitude dependent and dichotomous are used we observed noise induced extrinsic intermittency intermittent dynamics is characterized using power spectrum average and relative residence times on each precoupled attractors and probability distribution of time interval between successive switchings variation of probability distribution of state variables in poincare map is studied as a function of noise strength the effect of various noises is compared the occurrence of crisis induced and type i intermittencies are also presented

solitons as invariant tori in the perturbed nonlinear schro dinger equation abstract stabilities of a bound state of nonlinear schrodinger solitons are studied in the presence of some hamiltonian perturbations by means of numerical and perturbational methods behaviours of perturbed solitons are explained by perturbed hamiltonians and finite dimensional properties of solitons are found to be preserved for small hamiltonian perturbations

first order phase transition in a nonequilibrium growth process we introduce a simple continuous model for nonequilibrium surface growth the dynamics of the system is defined by the kardar parisi zhang equation with a morse like potential representing a short range interaction between the surface and the substrate the mean field solution displays a nontrivial phase diagram with a first order transition between a growing and a bound surface associated with a region of coexisting phases and a tricritical point where the transition becomes second order numerical simulations in three dimensions show quantitative agreement with mean field results and the features of the phase space are preserved even in two dimensions

interfacial growth in driven ginzburg landau models short and long time dynamics interfacial growth in driven systems is studied from the initial stage to the longtime regime numerical integrations of a ginzburg landan type equation with a new flux term introduced by an external field are presented the interfacial instabilities are induced by the external field from the numerical results we obtain the dispersion relation for the initial growth during the intermediate temporal regime fingers of a characteristic triangular shape could grow depending on the boundary conditions the final state corresponds to strips multifinger states or a one finger state the results for the initial growth are interpreted by means of surface driven and mullins sekerka instabilities the shape of the one finger state is explained in terms of the characteristic length introduced by the external field

stabilization of nonholonomic systems using isospectral flows in this paper we derive and analyze a discontinuous stabilizing feedback for a lie algebraic generalization of a class of kinematic nonholonomic systems introduced by brockett new directions in applied mathematics p hilton and g young eds springer verlag new york 1982 pp 11 27 the algorithm involves discrete switching between isospectral and norm decreasing flows we include a rigorous analysis of the convergence

exact time dependent solutions of the renyi fokker planck equation and the fokker planck equations related to the entropies proposed by sharma and mittal abstract exact time dependent solutions representing generalized one dimensional ornstein uhlenbeck processes are derived from nonlinear fokker planck equations and the corresponding diffusion processes are studied the corresponding systems are related to the renyi entropy and entropies proposed by sharma and mittal in the former case normal diffusion is found with a diffusion rate depending on the order of the renyi entropy in the latter case we find anomalous diffusion processes

on the internal resonance of multi degree of freedom systems with cubic non linearity abstract a new method of multiple scales procedure is used to analyze the forced responses of multiple degrees of freedom systems with cubic non linearity in which the internal resonance takes place simultaneously together with the forced resonances attention is focused on the superharmonic and subharmonic resonance caused by internal resonance as is near 1 or 2 where is the forcing frequency and 1 and 2 are the first and the second natural frequencies it is found that the responses are usually excitation level dependent and there is a critical excitation amplitude c in the case of near 1 when c the out of phase superharmonic resonance disappears in the case of near 2 when 0 c there are two branches of response when c one branch of responses vanishes the critical excitation amplitudes in different forced vibration are determined analytically in this paper

algorithms for controlling chaotic motion application for the bvp oscillator the bvp oscillator is a biologically and physically important dynamical system exhibiting chaotic motion phaselocking phenomenon and so on in this paper we investigate the controlling of chaos in this system both when periodic and constant currents are present we use the various control algorithms and investigate their effectiveness in particular we study the controlling by the following mechanisms i adaptive control algorithm ii weak periodic perturbations iii ott grebogi yorke method iv weak feedback control and v addition of noise also we show the suppression of chaos by numerical models

critical dynamics and fluctuations for a mean field model of cooperative behavior the main objective of this paper is to examine in some detail the dynamics and fluctuations in the critical situation for a simple model exhibiting bistable macroscopic behavior the model under consideration is a dynamic model of a collection of anharmonic oscillators in a two well potential together with an attractive mean field interaction the system is studied in the limit as the number of oscillators goes to infinity the limit is described by a nonlinear partial differential equation and the existence of a phase transition for this limiting system is established the main result deals with the fluctuations at the critical point in the limit as the number of oscillators goes to infinity it is established that these fluctuations are non gaussian and occur at a time scale slower than the noncritical fluctuations the method used is based on the perturbation theory for markov processes developed by papanicolaou stroock and varadhan adapted to the context of probability measure valued processes

synchronization and anti synchronization of chaos in an extended bonhoffer van der pol oscillator using active control abstract in this paper we investigate the complete synchronization and anti synchronization as of double scroll chaotic attractor exhibited by an extended bonhoffer van der pol bvp oscillator using active control technique in both synchronization schemes the oscillators show good transient performance while the as state is further shown to correspond with complete inverse synchronization numerical simulations are also presented to verify the theoretical results

non linear dynamics and chaos control of a physical pendulum with vibrating and rotating support the dynamic behavior of a physical pendulum system of which the support is subjected to both rotation and vertical vibration are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using lyapunov s direct method the conditions of stability of the relative equilibrium position can be determined melnikov s method is applied to identify the existence of chaotic motion the incremental harmonic balance method is used to find the stable and unstable periodic solutions for the strong non linear system by applying various numerical results such as phase portrait pioncare map time history and power spectrum analysis a variety of the periodic solutions and the phenomena of the chaotic motion can be presented the effects of the changes of parameters in the system could be found in the bifurcation and parametric diagrams further chaotic motion can be verified by using lyapunov exponent and lyapunov dimension the global analysis of basin boundary and fractal structure are observed by the modified interpolated cell mapping method besides non feedback control delayed feedback control adaptive control and variable structure control are used to control the chaos effectively

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

surface driven instability and enhanced relaxation in the dynamics of a nonequilibrium interface we determine the stability of a nonequilibrium interface between two coexisting solid phases in the presence of a weak external field starting at the coarsegrained cahn hilliard level we use the method of matched asymptotics to derive the macroscopic interfacial dynamics we then show that the external field leads to an instability due to flux along the interface in contrast with the more common mullins sekerka type instability which involves fluxes normal to the interface we also find that the external field produces an important modification of the gibbs thomson relation with these results we perform the linear stability analysis for an approximately flat interface if the field is tangent to the interface the modification of the gibbs thomson relation is important and the interface is stabilized if the field is normal to the interface the surface flux is important and the effect can be stabilizing or destabilizing but the orientational dependence is opposite what would be obtained if the mullins sekerka instability dominates numerical simulations are performed to study the effect of the surface current and are in agreement with our analytical results