brief paper novel decentralized adaptive strategies for the synchronization of complex networks this paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach in particular time varying feedback coupling gains are considered whose gradient is a function of the local synchronization error over each edge in the network it is shown that under appropriate conditions the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network the theoretical derivation is complemented by its validation on a set of representative examples

synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

hidden dynamics in models of discontinuity and switching a method of solving discontinuous differential equations is analyzed the central result generalizes filippov s method to nonlinear sliding modes exponentially small terms are shown to create novel switching dynamics the results are shown to account naturally for stiction static friction models random effects are shown to eliminate nonlinear terms under limited conditions a b s t r a c t sharp switches in behaviour like impacts stick slip motion or electrical relays can be modelled by differential equations with discontinuities a discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model the theory of piecewise smooth dynamics describes what happens assuming we can solve the system of equations across its discontinuity what this typically neglects is that effects which are vanishingly small outside the discontinuity can have an arbitrarily large effect at the discontinuity itself here we show that such behaviour can be incorporated within the standard theory through nonlinear terms and these introduce multiple sliding modes we show that the nonlinear terms persist in more precise models for example when the discontinuity is smoothed out the nonlinear sliding can be eliminated however if the model contains an irremovable level of unknown error which provides a criterion for systems to obey the standard filippov laws for sliding dynamics at a discontinuity

synchronizability of complex networks recent interest in the study of networks associated with complex systems has led to a better understanding of the factors and parameters relating the topology of the associated networks with the dynamics of the systems and in particular their synchronization in this paper by using known and new results from spectral graph theory we characterize relevant factors which affect the synchronization of complex networks

multisynchronization of coupled heterogeneous genetic oscillator networks via partial impulsive control this paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy the coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties the definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real considering that each genetic oscillator consists of a large number of biochemical molecules we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant theoretical analysis of multisynchronization is carried out by the control theory approach and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established at last numerical simulations are exploited to demonstrate the effectiveness of our results

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

blinking model and synchronization in small world networks with a time varying coupling the paper proposes a new type of small world networks of cells with chaotic behavior this network consists of a regular lattice of cells with constant 2k nearest neighbor couplings and time dependent on off couplings between any other pair of cells in each time interval of duration such a coupling is switched on with probability p and the corresponding switching random variables are independent for different links and for different times at each moment the coupling structure corresponds to a small world graph but the shortcuts change from time interval to time interval which is a good model for many real world dynamical networks it is to be distinguished from networks that have randomly chosen shortcuts fixed in time here we apply the connection graph stability method developed in the companion paper connection graph stability method for synchronized coupled chaotic systems see this issue to the study of global synchronization in this network with the time varying coupling structure in the case where the on off switching is fast with respect to the characteristic synchronization time of the network the synchronization thresholds are explicitly linked with the average path length of the coupling graph and with the probability p of shortcut switchings in this blinking model we prove that for the blinking model a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length short interactions between cells as in the blinking model are important in practice to cite prominent examples computers networked over the internet interact by sending packets of information and neurons in our brain interact by sending short pulses called spikes the rare interaction between arbitrary nodes in the network greatly facilitates synchronization without loading the network much in this respect we believe that it is more efficient than a structure of fixed random connections

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

instability in time delayed switched systems induced by fast and random switching abstract in this paper we consider a switched system comprising finitely or infinitely many subsystems described by linear time delayed differential equations and a rule that orchestrates the system switching randomly among these subsystems where the switching times are also randomly chosen we first construct a counterintuitive example where even though all the time delayed subsystems are exponentially stable the behaviors of the randomly switched system change from stable dynamics to unstable dynamics with a decrease of the dwell time then by using the theories of stochastic processes and delay differential equations we present a general result on when this fast and random switching induced instability should occur and we extend this to the case of nonlinear time delayed switched systems as well

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

stochastic synchronization in blinking networks of chaotic maps in this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on off couplings between any pair of nodes we focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold by projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics we establish a necessary and sufficient condition for stochastic synchronization based on the largest lyapunov exponent of the map and the spectral radius of such matrix this condition is further simplified by computing closed form results for the spectral properties of the moments of the graph laplacian associated to the intermittent coupling and using classical eigenvalue bounds we illustrate the main results through simulations on synchronization of chaotic henon maps

local analysis of co dimension one and co dimension two grazing bifurcations in impact microactuators impact microactuators rely on repeated collisions to generate gross displacements of a microelectromechanical machine element without the need for large applied forces their design and control rely on an understanding of the critical transition between non impacting and impacting long term system dynamics and the associated changes in system behavior in this paper we present three co dimension one characteristically distinct transition scenarios associated with grazing conditions for a periodic response of an impact microactuator a discontinuous jump to an impacting periodic response associated with parameter hysteresis a continuous transition to an impacting chaotic attractor and a discontinuous jump to an impacting chaotic attractor using the concept of discontinuity mappings a theoretical analysis is presented that predicts the character of each transition from a set of quantities that are computable in terms of system properties at grazing specifically we show how this analysis can be applied to predict the bifurcation behavior on neighborhoods of two co dimension two bifurcation points that separate the co dimension one bifurcation scenarios the predictions are validated against results from numerical simulations of a model impact microactuator

synchronization control for discrete time delayed dynamical networks with switching topology under actuator saturations this article is concerned with the synchronization control problem for a class of discrete time dynamical networks with mixed delays and switching topology the saturation phenomenon of physical actuators is specifically considered in designing feedback controllers by exploring the mixed delay dependent sector conditions in combination with the piecewise lyapunov like functional and the average dwell time switching a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances while the l l performance constraint is satisfied furthermore the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances second by using some congruence transformations the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities then three convex optimization problems are formulated regarding the disturbance tolerance the l l performance and the initial condition set respectively finally two simulation examples are given to show the effectiveness and merits of the proposed results

random walks in random environments random walks in random environments and their diffusion analogues have been a source of surprising phenomena and challenging problems especially in the non reversible situation since they began to be studied in the 1970s we review the model available results and techniques and point out several gaps in the understanding of these processes

brief paper convergence speed in distributed consensus over dynamically switching random networks characterizing convergence speed is one of the most important research challenges in the design of distributed consensus algorithms for networked multi agent systems in this paper we consider a group of agents that communicate via a dynamically switching random information network each link in the network which represents the directed undirected information flow between any ordered unordered pair of agents could be subject to failure with a certain probability hence we model the information flow using dynamically switching random graphs we characterize the convergence speed for the distributed discrete time consensus algorithm over a variety of random networks with arbitrary weights in particular we propose the asymptotic and per step mean square convergence factors as measures of the convergence speed and derive the exact value for the per step mean square convergence factor numerical examples are also given to illustrate our theoretical results

corner bifurcations in non smoothly forced impact oscillators abstract we consider an impacting mechanical system in which a particle at position u t impacts with a periodically moving obstacle at position z t the motion of which is non smooth in particular we look at corner events when u impacts with z very close to a point where z loses smoothness we show that this leads through a corner bifurcation to complex dynamics in u which can include periodic orbits of arbitrary period and period adding cascades by analysing associated maps close to the corner event we show that this dynamics can be understood in terms of the iterations of a two dimensional piecewise linear discontinuous map we also show some links between this analysis and the difficult problem of understanding the motion of three objects which may have simultaneous impacts

a unifying framework for the siso circle criterion and other quadratic stability criteria we present a result on the existence of a common quadratic lyapunov function for a pair of stable linear time invariant systems we show that this result characterizes generalizes and provides new perspectives on several well known stability results

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

global bounded synchronization of general dynamical networks with nonidentical nodes this note addresses the problem of synchronization for general dynamical networks with nonidentical nodes the coupling strength outer coupling configuration and inner connection in such networks are all time varying neither an equilibrium for each node nor a synchronization manifold is assumed to exist an estimate of the convergence domain for a general class of time varying nonlinear systems is given by introducing the average dynamics of all nodes and based on this estimate a criterion of global synchronization in the sense of boundedness of the maximum state deviation between nodes is developed an explicit bound of the maximum state deviation between nodes is obtained by the maximum difference between each node dynamics and the average dynamics the proposed criterion is an extension of several related synchronization criteria for the case of identical nodes to the case of nonidentical nodes

synchronization in complex networks with stochastically switching coupling structures synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed a novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed some sufficient condition for a network with general time varying coupling structure to reach complete synchronization is provided based on the general theorem networks with stochastically switching coupling structures is investigated in particular two kinds of stochastic switching coupling networks are addressed a independent and identically distributed switching processes and b markov jump processes in both cases some sufficient condition for almost sure synchronization of the networks is given also numerical simulations are provided to illustrate the theoretical results

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

discontinuity mappings for stochastic nonsmooth systems abstract for stability and bifurcation analysis involving recurrent behaviour such as periodic orbits it is important to be able to quantify how nearby trajectories behave by means of a local mapping in smooth systems these mappings can be computed using the system s variational equations for piecewise smooth or hybrid systems the same technique cannot be used without some corrections this is due to the fact that nearby trajectories can be topologically distinct because they can undergo different sequences of events associated with the system s discontinuity boundaries to account for this one can derive zero time discontinuity mappings associated with boundary interactions in this paper we derive zero time discontinuity mappings for piecewise smooth vector fields and hybrid dynamical systems in which the position of the discontinuity boundary has a stochastic component in particular we consider systems with stochastically oscillating boundaries and systems with stochastic imperfections on the discontinuity boundary

random talk random walk and synchronizability in a moving neighborhood network abstract we examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator the communication network topology changes randomly and is dictated by the agents locations in the lattice information sharing talking is possible only for geographically neighboring agents this complex system is a time varying jump nonlinear system we introduce the concept of long time expected communication network defined as the ergodic limit of a stochastic time varying network we show that if the long time expected network supports synchronization then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice

input to state stability and averaging of linear fast switching systems we consider the averaging method for stability of rapidly switching linear systems with disturbances we show that the notions of strong and weak averages proposed with partial strong average defined in this note play an important role in the context of switched systems using these notions of average we show that exponential input to state stability iss of the strong and the partial strong average system with linear gain imply exponential iss with linear gain of the actual system similarly exponential iss of the weak average guarantees an appropriate exponential derivative iss diss property for the actual system moreover using the lyapunov method we show that linear iss gains of the actual system and its average converge to each other as the switching rate is increased

dynamics of a two degree of freedom periodically forced system with a rigid stop diversity and evolution of periodic impact motions abstract a two degree of freedom periodically forced system with a clearance is considered the correlation between dynamic performance and system parameters is studied to find their feasible matching law the fundamental group of impact motions is defined which have the excitation period and differ by the number p of impacts the generation mechanism of complete and incomplete chattering impact vibration of the system is studied a series of singular points between any two adjacent fundamental impact motions are found at which real grazing and bare grazing bifurcation boundaries of one of them saddle node and period doubling bifurcation boundaries of the other alternately intersect and create two types of transition regions hysteresis and tongue shaped regions subharmonic impact motions are found to regularly appear in the tongue shaped regions based on the sampling ranges of parameters dynamics of the system is studied with emphasis on the influence of system parameters on impact velocities existence regions and correlative distribution of single impact periodic motions by multi parameter and multi performance co simulation analysis

a result on common quadratic lyapunov functions in this note we define strong and weak common quadratic lyapunov functions cqlfs for sets of linear time invariant lti systems we show that the simultaneous existence of a weak cqlf of a special form and the nonexistence of a strong cqlf for a pair of lti systems is characterized by easily verifiable algebraic conditions these conditions are found to play an important role in proving the existence of strong cqlfs for general lti systems

maximum performance at minimum cost in network synchronization we consider two optimization problems on synchronization of oscillator networks maximization of synchronizability and minimization of synchronization cost we first develop an extension of the well known master stability framework to the case of non diagonalizable laplacian matrices we then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the laplacian eigenvalues among the optimal networks we identify a subclass of hierarchical networks characterized by the absence of feedback loops and the normalization of inputs we show that most optimal networks are directed and non diagonalizable necessitating the extension of the framework we also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role

exclusive traveling waves for competitive reaction diffusion systems and their stabilities abstract we study the existence uniqueness and asymptotic behavior as well as the stability of a special kind of traveling wave solutions for competitive pde systems involving intrinsic growth competition crowding effects and diffusion the traveling waves are exclusive in the sense that as the variable goes to positive or negative infinity different species are close to extinction or carrying capacity we perform an appropriate affine transformation of the traveling wave equations into monotone form and construct appropriate upper and lower solutions by this means we reduce the existence proof to application of well known theory about monotone traveling wave systems cf a leung systems of nonlinear partial differential equations applications to biology and engineering mia kluwer boston 1989 j wu x zou traveling wave fronts of reaction diffusion systems with delay j dynam differential equations 13 2001 651 687 and i volpert v volpert v volpert traveling wave solutions of parabolic systems transl math monogr vol 140 amer math soc providence ri 1994 then by using spectral analysis of the linearization over the profile we prove the orbital stability of the traveling wave in some banach spaces with exponentially weighted norm furthermore we show that the introduction of some weight is necessary in the sense that in general traveling wave solutions with initial perturbations in the unweighted space c 0 are unstable cf i volpert v volpert v volpert traveling wave solutions of parabolic systems transl math monogr vol 140 amer math soc providence ri 1994 and d henry geometric theory of semilinear parabolic equations lecture notes in math vol 840 springer verlag new york 1981

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

a discontinuity geometry view of the relationship between saddle node and grazing bifurcations abstract in this study we will introduce a topological approach termed as discontinuity geometry for both analysis and visualization of the dynamics of periodically forced impact oscillators after a brief outline of the methodology and the general representation of trajectories with impacts the framework will be used to analyse grazing bifurcations in particular it will be used to geometrically explain why there is sometimes a saddle node bifurcation present in the vicinity of grazing bifurcations and why it is sometimes absent

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

bifurcations in nonsmooth dynamical systems a review is presented of the one parameter nonsmooth bifurcations that occur in a variety of continuous time piecewise smooth dynamical systems motivated by applications a pragmatic approach is taken to defining a discontinuity induced bifurcation dib as a nontrivial interaction of a limit set with respect to a codimension one discontinuity boundary in phase space only dibs that are local are considered that is bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows three classes of systems are considered involving either state jumps jumps in the vector field or jumps in some derivative of the vector field a rich array of dynamics are revealed involving the sudden creation or disappearance of attractors jumps to chaos bifurcation diagrams with sharp corners and cascades of period adding for each kind of bifurcation identified where possible a kind of normal form or discontinuity mapping dm is given together with a canonical example and an application the goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators impact oscillators dc dc converters and problems in control theory

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

the geometry of generic sliding bifurcations using the singularity theory of scalar functions we derive a classification of sliding bifurcations in piecewise smooth flows these are global bifurcations which occur when distinguished orbits become tangent to surfaces of discontinuity called switching manifolds the key idea of the paper is to attribute sliding bifurcations to singularities in the manifold s projection along the flow namely to points where the projection contains folds cusps and two folds saddles and bowls from the possible local configurations of orbits we obtain sliding bifurcations in this way we derive a complete classification of generic one parameter sliding bifurcations at a smooth codimension one switching manifold in n dimensions for n ge3 we uncover previously unknown sliding bifurcations all of which are catastrophic in nature we also describe how the method can be extended to sliding bifurcations of codimension two or higher

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

geometrical quasi dissipativity and boundedness property for switched discrete time nonlinear systems this paper studies geometrical quasi dissipativity and boundedness properties for switched discrete time nonlinear systems first a new concept of geometrical quasi dissipativity for a switched di

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

control of near grazing dynamics in impact oscillators a method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontinuities in particular it is shown that a discrete linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact the implementation relies on a local analysis of the near grazing dynamics using the concept of discontinuity mappings numerical results are presented for a linear and a nonlinear oscillator

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

a maximum principle for diffusive lotka volterra systems of two competing species abstract using an elementary approach we establish a new maximum principle for the diffusive lotka volterra system of two competing species which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function the first derivative of another function and a quadratic nonlinearity this maximum principle gives a priori estimates for the total mass of the two species moreover applying it to the system of three competing species leads to a nonexistence theorem of traveling wave solutions

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

lyapunov based approach to multiagent systems with switching jointly connected interconnection this note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies neighbor based rules are adopted to realize local control strategies for these continuous time autonomous agents described by double integrators although the interagent connection structures vary over time and related graphs may not be connected a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed lyapunov based approach and related space decomposition technique

connection graph stability method for synchronized coupled chaotic systems this paper elucidates the relation between network dynamics and graph theory a new general method to determine global stability of total synchronization in networks with different topologies is proposed this method combines the lyapunov function approach with graph theoretical reasoning in this context the main step is to establish a bound on the total length of all paths passing through an edge on the network connection graph in particular the method is applied to the study of synchronization in rings of 2k nearest neighbor coupled oscillators a rigorous bound is given for the minimum coupling strength sufficient for global synchronization of all oscillators this bound is explicitly linked with the average path length of the coupling graph contrary to the master stability function approach developed by pecora and carroll the connection graph stability method leads to global stability of synchronization and it permits not only constant but also time dependent interaction coefficients in a companion paper blinking model and synchronization in small world networks with a time varying coupling see this issue this method is extended to the blinking model of small world networks where in addition to the fixed 2 k nearest neighbor interactions all the remaining links are rapidly switched on and off independently of each other

stability of switched systems on randomly switching durations with random interaction matrices in this paper we investigate the almost sure stability of switched systems on randomly switching durations simultaneously with randomly switching interaction matrices we not only allow the interaction matrix on each switching duration to take values randomly from either a countable an uncountable or even an unbounded state space but also allow the corresponding probability density function to be time varying with the switching we provide an example to show the difference between the almost sure stability and the moment stability then we establish several practical stability criteria for switched systems which may have linear or nonlinear subsystems these stability criteria also enable us to find suitable conditions for realizing almost sure synchronization in complex networks such as small world networks with both randomly switching durations and a few switching couplings that take values randomly in either an uncountable or an unbounded state space

mixed h_2 h_ infty state estimation for discrete time switched complex networks with random coupling strengths through redundant channels this article investigates the mixed h 2 h infty state estimation problem for a class of discrete time switched complex networks with random coupling strengths through redundant communication channels a sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths a redundant channel based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator the purpose of the addressed problem is to design a state estimator for each node such that the error dynamics achieves both the stochastic stability with probability 1 and the prespecified mixed h 2 h infty performance requirement by using the switched system theory an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed h 2 h infty performance index the desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems a numerical example is provided to illustrate the validity of the proposed estimation scheme