an infinity norm bound for the inverse of dashnic zusmanovich type matrices with applications abstract an upper bound for the infinity norm for the inverse of dashnic zusmanovich type matrices is given it is proved that the upper bound is sharper than the well known varah s bound for strictly diagonally dominant matrices by introducing a new subclass of p matrices dashnic zusmanovich type b matrices dz type b matrices and using the proposed infinity norm bound an error bound is given for the linear complementarity problems of dz type b matrices we also give a new pseudospectra localization to measure the distance to instability

strange nonchaotic attractors with wada basins a b s t r a c t we demonstrate strange nonchaotic attractors with wada basins snaswb and verify the abundance of snaswb in a quasiperiodically forced holmes map we identify the routes to the creation of the snaswb in a two parameter space the snaswb are characterized by the maximal lyapunov exponent by the estimation of the phase sensitivity exponent and by the singular continuous spectra we observe that the snas basins are totally wada basins in a large range of parameters the topological structures of the snas wada basins are distinguished by the basin cell method we investigate the underlying mechanism for the abundance of snaswb which is responsible for different types of basin cell in the absence of forcing this suggests that the snas cannot be predicted reliably for specific initial conditions these snaswb can thus be expected to occur more commonly in dynamical systems

fractal basin boundaries abstract basin boundaries for dynamical systems can be either smooth or fractal this paper investigates fractal basin boundaries one practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes the structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected examples and discussion of both types of structures are given and it appears that fractal basin boundaries should be common in typical dynamical systems lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed

succinct representation of regular languages by boolean automata ii abstract boolean automata are a generalization of finite automata in the sense that the next state the result of the transition function given a state and a letter is not just a single state deterministic automata or a set of states nondeterministic automata but a boolean function of the states boolean automata accept precisely the regular languages also they correspond in a natural way to certain language equation involving complementation as well as to sequential networks in a previous note we showed that for every n 1 there exists a boolean automaton b n with n states such that the smallest deterministic automaton for the same language has 2 2 n states in the present note we will show a precisely attainable lower bound on the succinctness of representing regular languages by boolean automata namely we will show that for every n 1 there exists a reduced automaton d n with n states such that the smallest boolean automaton accepting the same language has also n states

error bounds for linear complementarity problems of db matrices doubly b matrices db matrices which properly contain b matrices are introduced by pena 2003 2 in this paper we present error bounds for the linear complementarity problem when the matrix involved is a db matrix and a new bound for linear complementarity problem of a b matrix the numerical examples show that the bounds are sharp

computation of error bounds for p matrix linear complementarity problems we give new error bounds for the linear complementarity problem where the involved matrix is a p matrix computation of rigorous error bounds can be turned into a p matrix linear interval system moreover for the involved matrix being an h matrix with positive diagonals an error bound can be found by solving a linear system of equations which is sharper than the mathias pang error bound preliminary numerical results show that the proposed error bound is efficient for verifying accuracy of approximate solutions

fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions we consider the existence of robust strange nonchaotic attractors in a simple class of quasiperiodically forced systems rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box counting dimension d 0 is larger than their information dimension d 1 by 1 i e d 0 d 1 1 we also show how this property is manifested in numerical experiments

wada basin boundaries and basin cells in dynamical systems examples are common in which two or more attractors coexist and in such cases the basin boundary is nonempty we consider a two dimensional diffeomorphism f that is f is an invertible map and both f and its inverse are differentiable with continuous derivatives which has at least three basins fractal basin boundaries contain infinitely many periodic points generally only finitely many of these periodic points are outermost on the basin boundary that is accessible from a basin for many systems all accessible points lie on stable manifolds of periodic points a point x on the basic boundary is a wada point if every open neighborhood of x has a nonempty intersection with at least three different basins we call the boundary of a basin a wada basin boundary if all its points are wada points our main goal is to have definitions and hypotheses for wada basin boundaries that can be verified by computer the basic notion basin cell will play a fundamental role in our results for numerical verifications assuming each accessible point on the boundary of a basin b is on the stable manifold of some periodic orbit we show that partial derivative b over bar is a wada basin boundary if the unstable manifold of each of its accessible periodic orbits intersects at least three basins in addition we find conditions for basins b 1 b 2 b n n greater than or equal to 3 to satisfy partial derivative b over bar 1 partial derivative b over bar 2 partial derivative b over bar n our results provide numerically verifiable conditions guaranteeing that the boundary of a basin is a wada basin boundary our examples make use of an existing numerical procedure for finding the accessible periodic points on the basin boundary and another procedure for plotting stable and unstable manifolds to verify the existence of wada basin boundaries

singularities in vibro impact dynamics abstract the non differentiable nature of vibro impact dynamics can lead to breakdown of the global stable manifold theorem applicable to smooth dynamical systems in one dimensional periodically excited system the breakdown leads to the shredding of the stable manifolds and this process is analyzed in detail bodily translation of filaments of stable manifolds can lead to homoclinic intersections and this topic is discussed in the context of a new bifurcation due to re entrance shredding leads to a strong similarity between the geometries of the singular subspaces and the geometries of homoclinic tangles and strange attracting sets

quasiperiodically driven maps in the low dissipation limit received 24 september 2012 revised manuscript received 18 february 2013 published 11 march 2013 we study the quasiperiodically driven henon and standard maps in the weak dissipative limit in the absence of forcing there are a large number of coexisting periodic attractors although chaotic attractors can also be found these typically have vanishingly small basins of attraction quasiperiodic forcing reduces the multistability in thesystem and as the bifurcation parameter is varied strange nonchaotic attractors snas are created the attractorbasin for snas appears to be the largest among those of all coexisting attractors at such a transition doi 10 1103 physreve 87 034901 pacs number s 05

upper bounds for the infinity norm of the inverse of sdd and s sdd matrices an easily calculable upper bound for the infinity norm of the inverse of s strictly diagonally dominant s sdd matrices introduced by gao and wang in 1992 is obtained in this paper applying that bound to sdd matrices we improve the varah bound we also introduce an iterative procedure for obtaining sharper bounds accompanied with some open questions

state complexity of combined operations we study the state complexity of combined operations two particular combined operations are studied star of union and star of intersection it is shown that the state complexity of a combined operation is not necessarily similar to the combination of the individual state complexities of the participating operations

codimension 2 hopf bifurcation of a two degree of freedom vibro impact system abstract codimension 2 hopf bifurcation problem of a two degree of freedom system vibrating against a rigid surface is investigated in this paper the four dimensional poincare map of the vibro impact system is reduced to a two dimensional normal form by virtue of a center manifold reduction and a normal form technique then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of codimension 2 hopf bifurcation of the vibro impact system the quasi periodic response of the system by theoretical analysis is well supported by numerical simulations it is shown that there exists codimension 2 hopf bifurcation in multi degree of freedom vibro impact systems the codimension 2 tori doubling phenomenon and the routes of quasi periodic impacts to chaos are reported briefly

error bounds for the linear complementarity problem with a p matrix abstract we introduce a fundamental quantity associated with a p matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the p type we also obtain upper and lower bounds for the quantity introduced

multistability noise and attractor hopping the crucial role of chaotic saddles we investigate the hopping dynamics between different attractors in a multistable system under the influence of noise using symbolic dynamics we find a sudden increase of dynamical entropies when a system parameter is varied this effect is explained by a bifurcation involving two chaotic saddles we also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

fractalization route to strange nonchaotic dynamics in the fractalization route for the formation of strange nonchaotic attractors sna s in quasiperiodically driven nonlinear dynamical systems a smooth torus gradually becomes a fractal as the forcing amplitude is increased while the lyapunov exponent remains nonpositive using techniques introduced by kim et al to identify unstable sets in sna s we study torus fractalization in a sequence of approximations wherein the quasiperiodic drive is replaced by periodic forcing of increasing period this allows us to identify an unstable set embedded in the attractor in the periodically forced system we show that there is a cascade of attractor merging crises and argue that the quasiperiodic analogue of such crises causes fractalization of tori to create sna s

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

dynamical behavior of vibro impact machinery near a point of codimension two bifurcation a dual component system with vibro impact is considered local codimension two bifurcation of maps involving a real eigenvalue and a complex conjugate pair escaping the unit circle simultaneously is analyzed by using the center manifold and normal form method for maps the period n single impact motion and poincare map of the vibro impact system are derived analytically stability and local bifurcation of single impact periodic motion are analyzed by using the poincare map a center manifold theorem technique is applied to reduce the poincare map to a three dimensional one and the normal form map associated with the codimension two bifurcation is obtained local behavior of the dual component system with vibro impact near the point of codimension two bifurcation is analyzed it is found that near the point of codimension two bifurcation there exists not only hopf bifurcation of period one single impact motion but also hopf bifurcation of period two double impact motion period doubling bifurcation of period one single impact motion commonly exists near the point of codimension two bifurcation however no period doubling cascade emerges due to change of the type of period two fixed points and occurrence of hopf bifurcation associated with period two fixed points the period two fixed points are symmetrical about the corresponding period one point the results from simulation show that the attracting invariant circles associated with period two points are symmetrical about the corresponding period one point near the value of hopf bifurcation of period two points two actual examples the impact forming machinery and inertial shaker are chosen to analyze further the phenomena of codimension two bifurcation of maps and local bifurcation analysis and numerical simulation are carried out to unfold dynamical behavior of these vibro impact systems near the points of codimension two bifurcations

an efficient qr based method for the computation of lyapunov exponents abstract an efficient and numerically stable method to determine all the lyapunov characteristic exponents of a dynamical system is developed numerical experiments are presented highlighting some aspects of convergence accuracy and efficiency in the computation of the lyapunov characteristic exponents

infimum of error bounds for linear complementarity problems of σ sdd and σ1 ssd matrices abstract in 2013 18 garcia esnaola and pena presented error bounds for the linear complementarity problems of sdd and 1 ssd matrices respectively these bounds all involve a parameter on an open interval it is shown in this paper that the infimum of these error bounds as a function of the parameter exists and then is determined numerical examples are given to verify the theoretical results

strange nonchaotic attractors in the quasiperiodically forced logistic map different mechanisms for the creation of strange nonchaotic dynamics in the quasiperiodically forced logistic map are studied these routes to strange nonchaos are characterized through the behavior of the largest nontrivial lyapunov exponent as well as through the characteristic distributions of finite time lyapunov exponents strange nonchaotic attractors can be created at a saddle node bifurcation when the dynamics shows type i intermittency this intermittent transition which is studied in detail is characterized through scaling exponents band merging crises through which dynamics remains nonchaotic are also studied and correspondence is made with analogous behavior in the unforced logistic map robustness of these phenomena with respect to additive noise is investigated s1063 651x 98 10302 1

bubbling route to strange nonchaotic attractor in a nonlinear series lcr circuit with a nonsinusoidal force we identify an unconventional route to the creation of a strange nonchaotic attractor sna in a quasiperiodically forced electronic circuit with a nonsinusoidal square wave force as one of the quasiperiodic forces through numerical and experimental studies we find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force the bubbles then enlarge and get increasingly wrinkled as a function of the control parameter finally the bubbles get extremely wrinkled while the remaining parts of the strands of the torus remain largely unaffected resulting in the creation of the sna we term this the bubbling route to the sna we characterize and confirm this creation from both experimental and numerical data using maximal lyapunov exponents and their variance poincar e maps fourier amplitude spectra and spectral distribution functions we also strongly confirm the creation of a sna via the bubbling route by the distribution of the finite time lyapunov exponents

state complexity of combined operations for suffix free regular languages we investigate the state complexity of combined operations for suffix free regular languages suffix free deterministic finite state automata have a unique structural property that is crucial for obtaining the precise state complexity of basic operations based on the same property we establish the state complexity of four combined operations star of union star of intersection star of reversal and star of catenation in the case of star of intersection we only have an upper bound and the lower bound is open

state complexity of basic operations on suffix free regular languages we investigate the state complexity of basic operations for suffix free regular languages the state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worst case for the minimal deterministic finite state automaton that accepts the language obtained from the operation we establish the precise state complexity of catenation kleene star reversal and the boolean operations for suffix free regular languages

control of multistate hopping intermittency in multistable regimes noise can create multistate hopping intermittency i e intermittent transitions among coexisting stable attractors we demonstrate that a small periodic perturbation can significantly control such hopping intermittency by control we imply a qualitative change in the probability distribution of occupation in the phase space around the stable attractors in other words if the uncontrolled system exhibits a preference to stay around a given attractor say a in comparison to another attractor say b the control perturbation creates a contrasting scenario so that attractor b is most frequently visited and consequently the occupation probability becomes maximum around b instead of a the control perturbation works in the following way it destroys attractor a by boundary crisis while attractor b remains stable as a result even if the system is pushed by noise into the erstwhile basin of attractor a the system does not remain there for long and therefore stays longer around attractor b significantly such a change in the intermittent scenario can be obtained by a small amplitude and slow periodic perturbation the control is theoretically demonstrated with two standard models namely lorenz equations for autonomous systems and the periodically driven damped toda oscillator for nonautonomous systems recent experiments with a cavity loss modulated mathrm c mathrm o 2 laser and an analog circuit of lorenz equations have validated our theoretical demonstrations excellently

escape from attracting sets in randomly perturbed systems the dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science previous studies of escape in chaotic systems have rather focused on the case of unbounded noise usually assumed to have gaussian distribution in this paper we address the problem of escape induced by bounded noise we show that the dynamics of escape from an attractor s basin is equivalent to that of a closed system with an appropriately chosen hole using this equivalence we show that there is a minimum noise amplitude above which escape takes place and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition we verify our analytical predictions through numerical simulations of two well known two dimensional maps with noise

periodic motions and global bifurcations of a two degree of freedom system with plastic vibro impact a two degree of freedom d o f impact system with proportional damping is considered the maximum displacement of one of the masses is limited to a threshold value by a rigid wall which gives rise to a non linearity in the system a limiting case of a dynamical problem arising in the mechanical systems with amplitude constraints is investigated for the perfectly plastic vibro impact case dynamics of a two degree of freedom vibratory system contacting a single stop is represented by a three dimensional map existence and stability of period n single impact motions are analyzed by analytical and numerical methods it is shown that the vibro impact system may exhibit two different types of periodic motions due to the piecewise property of the map transitions of two types of period n single impact motions are demonstrated the singularities of the poincare map caused by grazing boundary motion of the impact oscillator are considered due to the piecewise discontinuities and singularities of the map the vibro impact system is shown to undergo period doubling bifurcations followed by complex sequence of transitions in which the period doubling cascades do not occur and extremely long periodic and chaotic motions are generated directly with the motions with grazing boundary occurring finally the influence of system parameters on periodic impacts and global bifurcations is discussed

general approach to the localization of unstable periodic orbits in chaotic dynamical systems we present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system our approach allows us to locate in an efficient way the unstable cycles of in principle arbitrary length with a high accuracy based on a universal set of linear transformations the originally unstable periodic orbits are transformed into stable ones and can consequently be detected and analyzed easily this method is applicable to dynamical systems of any dimension and requires no preknowledges with respect to the solutions of the original chaotic system as an example of application of our method we investigate the ikeda attractor in some detail

singular continuous spectra in dissipative dynamics we demonstrate the occurrence of regimes with singular continuous fractal fourier spectra in autonomous dissipative dynamical systems the particular example is an ordinary differential equation system at the accumulation points of bifurcation sequences associated with the creation of complicated homoclinic orbits two different mechanisms responsible for the appearance of such spectra are proposed in the first case when the geometry of the attractor is symbolically represented by the thue morse sequence both the continuous time process and its discrete poincar e map have singular power spectra the other mechanism is due to the logarithmic divergence of the first return times near the saddle point here the poincar e map possesses the discrete spectrum while the continuous time process displays the singular one a method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual fourier analysis technique

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

renormalization of correlations and spectra of a strange non chaotic attractor we study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum we show that the symbolic dynamics is exactly described by a language generated from a suitable inflation rule we derive renormalization transformations for both the power spectrum and the autocorrelation function thus obtaining a quantitative description of the scaling properties the multifractal nature of the spectrum is also discussed

hopf bifurcation of a two degree of freedom vibro impact system abstract the bifurcation problem of a two degree of freedom system vibrating against a rigid surface is studied in this paper it is shown that there exist hopf bifurcations in the vibro impact systems with two or more degrees of freedom under suitable system parameters in the paper a centre manifold theorem technique is applied to reduce the poincare map of the vibro impact system to a two dimensional one and then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of hopf bifurcation of the vibro impact system the theoretical solutions are verified by numerical computations the quasi periodic response of the system represented by invariant circles in the projected poincare sections is obtained by numerical simulations and routes of quasi periodic impacts to chaos are stated briefly

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

on the state complexity of reversals of regular languages we compare the number of states between minimal deterministic finite automata accepting a regular language and its reversal mirror image in the worst case the state complexity of the reversal is 2n for an n state language we present several classes of languages where this maximal blow up is actually achieved and study the conditions for it in the case of finite languages the maximal blow up is not possible but still a surprising variely of different growth types can be exhibited

error bounds for the linear complementarity problem with a σ sdd matrix abstract we give new error bounds for the linear complementarity problem when the involved matrix is a sdd matrix with positive diagonals the new bounds can improve considerably other previous bounds we also find a subclass of sdd matrices for which the new bound is very simple

error bounds for linear complementarity problems of s nekrasov matrices and b s nekrasov matrices abstract an error bound involving a parameter which does not always work for the linear complementarity problem lcp when the involved matrices are s nekrasov matrices is provided by m garcia esnaola and j m pena 2014 in this paper a new error bound for the lcp of s nekrasov matrices is presented which depends only on the entries of the involved s nekrasov matrices based on the obtained results we also give an error bound for the lcp of b s nekrasov matrices

basins of wada abstract we describe situations in which there are several regions more than two with the wada property namely that each point that is on the boundary of one region is on the boundary of all we argue that such situations arise even in studies of the forced damped pendulum where it is possible to have three attractor regions coexisting and the three basins of attraction have the wada property

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

bifurcations and transitions in the quasiperiodically driven logistic map abstract we discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map this system can have strange nonchaotic attractors snas in addition to chaotic and regular attractors on snas the dynamics is aperiodic but the largest lyapunov exponent is nonpositive there are a number of different transitions that occur here from periodic attractors to snas from snas to chaotic attractors etc we describe some of these transitions by examining the behavior of the largest lyapunov exponent distributions of finite time lyapunov exponents and the invariant densities in the phase space

synchronization of strange nonchaotic attractors strange nonchaotic attractors snas which are realized in many quasiperiodically driven nonlinear systems are strange geometrically fractal but nonchaotic the largest nontrivial lyapunov exponent is negative two such identical independent systems can be synchronized by in phase driving because of the negative lyapunov exponent the systems converge to a common dynamics which because of the strangeness of the underlying attractor is aperiodic this feature which is robust to external noise can be used for applications such as secure communication a possible implementation is discussed and its performance is evaluated the use of snas rather than chaotic attractors can offer some advantages in experiments involving synchronization with aperiodic dynamics

experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit we have identified the three prominent routes namely heagy hammel fractalization and intermittency routes and their mechanisms for the birth of strange nonchaotic attractors snas in a quasiperiodically forced electronic system constructed using a negative conductance series lcr circuit with a diode both numerically and experimentally the birth of snas by these three routes is verified from both experimental and their corresponding numerical data by maximal lyapunov exponents and their variance poincar e maps fourier amplitude spectrum spectral distribution function and finite time lyapunov exponents although these three routes have been identified numerically in different dynamical systems the experimental observation of all these mechanisms is reported here in a single second order electronic circuit

birth of strange nonchaotic attractors due to interior crisis abstract we study the interior crisis in the period 3 window of the quasiperiodically forced logistic map two routes from quasiperiodicity to chaos involving strange nonchaotic attractors sna are discovered along one route we observe a sudden widening of the sna this is similar to the interior crisis in chaotic systems along the other route we find a direct transition from an invariant curve to a strange nonchaotic attractor exactly at the interior crisis point this is a new mechanism of the appearance of strange nonchaotic attractors beyond the interior crisis the temporal behavior can be described as a crisis induced intermittency whose scaling behavior is discussed

correlations and spectra of strange non chaotic attractors we consider correlations and spectra of strange nonchaotic attractors in quasiperiodically driven nonlinear systems it is demonstrated that a self similar autocorrelation function and a singular continuous spectrum may be observed in such systems the properties of correlations and spectra depend very subtly on the rotation number of the quasiperiodic force and on the parameters of the system for some parameter values the usual discrete spectrum is restored

interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map mechanisms and their characterizations a simple quasiperiodically forced one dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors snas in a two parameter a ensuremath f space the routes include transitions to chaos via snas from both a one frequency torus and a period doubled torus in the former case we identify the fractalization and type i intermittency routes in the latter case we point out that at least four distinct routes for the truncation of the torus doubling bifurcation and the creation of snas occur in this model in particular the formation of snas through heagy hammel fractalization and type iii intermittent mechanisms is described in addition it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the attractor which tames the growth of period doubling bifurcation takes place creating the sna the snas created through different mechanisms are characterized by the behavior of the lyapunov exponents and their variance by the estimation of the phase sensitivity exponent and through the distribution of finite time lyapunov exponents

double neimark sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops abstract a multidegree of freedom system having symmetrically placed rigid stops and subjected to periodic excitation is considered the system consists of linear components but the maximum displacement of one of the masses is limited to a threshold value by the symmetrical rigid stops repeated impacts usually occur in the vibratory system due to the rigid amplitude constraints such models play an important role in the studies of mechanical systems with clearances or gaps double neimark sacker bifurcation of the system is analyzed by using the center manifold and normal form method of maps the period one double impact symmetrical motion and homologous disturbed map of the system are derived analytically a center manifold theorem technique is applied to reduce the poincare map to a four dimensional one and the normal form map associated with double neimark sacker bifurcation is obtained the bifurcation sets for the normal form map are illustrated in detail local behavior of the vibratory systems with symmetrical rigid stops near the points of double neimark sacker bifurcations is reported by the presentation of results for a three degree of freedom vibratory system with symmetrical stops the existence and stability of period one double impact symmetrical motion are analyzed explicitly also local bifurcations at the points of change in stability are analyzed thus giving some information on dynamical behavior near the points of double neimark sacker bifurcations near the value of double neimark sacker bifurcation there exist period one double impact symmetrical motion and quasi periodic impact motions the quasi periodic impact motions are represented by the closed circle and tire like attractor in projected poincare sections with change of system parameters the quasi periodic impact motions usually lead to chaos via tire like torus doubling

fractalization of a torus as a strange nonchaotic attractor fractalization of a torus and its transition to chaos in a quasiperiodically forced logistic map is reinvestigated in relation to a strange nonchaotic attractor with the aid of a functional equation for the invariant curve the existence of a fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor as well as the fourier mode analysis mechanisms of the onset of a fractal torus and the transition to chaos are studied in connection with the intermittency

doubling bifurcations of destroyed t 2 tori abstract two duffing oscillators driven with incommensurate frequencies and coupled additively are investigated with this system we observe a host of complex behavior which compete with each other in parameter space in particular the period doubling of an attracting t 2 torus and the destruction of a t 2 torus as the parameters are varied along a curve in parameter space we observe period doubling bifurcations of a destroyed t 2 torus this phenomenon is studied in greater detail via a simple recursive map

invariant graphs for forced systems abstract many applications of nonlinear dynamics involve forced systems we consider the case where for a fixed input the driven system is contracting this is for instance the situation in certain classes of filters and in the study of synchronization when such contraction is uniform it is well known that there exists a globally attracting invariant set which is the graph of a function from the driving state space to the driven state space if the contraction is sufficiently strong then is smooth we describe the theoretical framework for such results and discuss a number of applications to the filtering of time series to synchronization and to quasiperiodically forced systems we go on to give recent generalizations to the case of non uniform contraction that is contraction measured by lyapunov exponent like quantities we conclude with a number of new results for quasiperiodic forcing a corollary of these is that a strange non chaotic attractor for such a system cannot be the graph of a continuous function nor roughly speaking can it have as open attracting neighbourhood in other words its closure must contain some repelling orbits

on some properties of nearly conservative dynamics of ikeda map and its relation with the conservative case abstract the behavior of the well known ikeda map with very weak dissipation so called nearly conservative case is investigated the changes in the bifurcation structure of the parameter plane while decreasing the dissipation are revealed it is shown that when the dissipation is very weak the system demonstrates an intermediate type of dynamics combining the peculiarities of conservative and dissipative dynamics the correspondence between the trajectories in the phase space in the conservative case and the transformations of the set of initial conditions in the nearly conservative case has been obtained the dramatic increase of the number of coexisting low period attractors and the extraordinary growth of the transient time while the dissipation decreases have been revealed the method of plotting a bifurcation tree for the set of initial conditions has been used to classify the existing attractors by their structure also it was shown that most of the coexisting attractors are destroyed by rather small external noise and the transient time in noisy driven systems increases still more the new method of two parameter analysis for conservative systems was proposed

period doubling bifurcations and universality in conservative systems we have studied numerically a sequence of period doubling bifurcations of periodic orbits of henon s conservative two dimensional mapping in agreement with other recent studies we also find evidence that such sequences possess universality properties similar to the ones observed for dissipative systems the corresponding universal constants however have significantly different values in each case we suggest that a possible explanation for this discrepancy may be the fact that conservative systems owing to their measure preserving property do not become asymptotically one dimensional as dissipative systems do

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

boundary crisis in quasiperiodically forced systems abstract we study boundary crisis in quasiperiodically forced dissipative systems using the henon map as a characteristic example the crisis is due to a homoclinic tangency of the stable and unstable manifolds of an accessible invariant circle of saddle type on the basin boundary of the attractor numerical evidence shows that the type of boundary crisis can change as the saddle circle loses its accessibility due to the quasiperiodic forcing this implies the existence of codimension two double crisis vertices where a curve of boundary crisis and a curve of interior crisis meet we argue that bifurcation points of higher codimension must exist in the full parameter space

a comparison of error bounds for linear complementarity problems of h matrices we give new error bounds for the linear complementarity problem when the involved matrix is an h matrix with positive diagonals we find classes of h matrices for which the new bounds improve considerably other previous bounds we also show advantages of these new bounds with respect the computational cost a new perturbation bound of h matrices linear complementarity problems is also presented

torus doubling bifurcations and strange nonchaotic attractors in a vibro impact system whether strange nonchaotic attractors snas can occur typically in dynamical systems other than quasiperiodically driven systems has been an open problem here we show that the snas can be induced by the interruption of torus doubling bifurcation in a periodically driven vibro impact system it is found that the creation of snas occurs due to the collision of doubled torus with some unstable periodic orbits based on the poincare map technique two types of codimension 3 bifurcations are represented and typical torus doubling bifurcations can occur in the neighborhood of these bifurcation points we use the singular continuous fourier spectrum and its scaling to verify the strangeness nondifferentiability of the attractors the implicitly transcendental map is used to calculate the largest lyapunov exponent by qr based algorithm which ensures that the underlying dynamics with nonpositive lyapunov exponents is nonchaotic the associated mechanism is described for the creation of snas through detecting unstable periodic orbits from poincare map series

mechanism for the intermittent route to strange nonchaotic attractors intermittent strange nonchaotic attractors snas appear typically in quasiperiodically forced period doubling systems as a representative model we consider the quasiperiodically forced logistic map and investigate the mechanism for the intermittent route to snas using rational approximations to the quasiperiodic forcing it is found that a smooth torus transforms into an intermittent sna via a phase dependent saddle node bifurcation when it collides with a new type of ring shaped unstable set

milnor strange nonchaotic attractor with complex basin of attraction the transcritical blowout bifurcation of a quasiperiodic torus on an invariant subspace is studied in this paper we found that the strange nonchaotic attractor sna beyond the blowout bifurcation is only a weak attractor in the sense of milnor this is different from the popularly studied case where the milnor attractor is a chaotic one with a riddled basin of attraction characters of this milnor sna and the influence of a random noise are studied

criteria for generalized diagonally dominant matrices and m matrices abstract we provide new necessary and sufficient conditions for verifying strictly generalized diagonally dominant matrices by applying the inverse of a partitioned matrix and obtain some criteria for identifying nonsingular m matrices