stochastic resonance in an ensemble of bistable systems under stable distribution noises and nonhomogeneous coupling in this paper stochastic resonance of an ensemble of coupled bistable systems driven by noise having an stable distribution and nonhomogeneous coupling is investigated the stable distribution considered here is characterized by four intrinsic parameters 0 2 is called the stability parameter for describing the asymptotic behavior of stable densities 1 1 is a skewness parameter for measuring asymmetry 0 is a scale parameter for measuring the width of the distribution and is a location parameter for representing the mean value it is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths we show that the stability parameter and the scale parameter can be well selected to generate resonant effects in response to external signals in addition the interplay between the skewness parameter and the location parameter on the resonance effects is also studied we further show that the asymmetry of a l evy stable distribution resulting from the skewness parameter and the location parameter can enhance the resonance effects both theoretical analysis and simulation are presented to verify the results of this paper

contractivity of linear fractional transformations one possible approach to exact real arithmetic is to use linear fractional transformations lfts to represent real numbers and computations on real numbers recursive expressions built from lfts are only convergent i e denote a well defined real number if the involved lfts are sufficiently contractive in this paper we define a notion of contractivity for lfts it is used for convergence theorems and for the analysis and improvement of algorithms for elementary functions

most probable dynamics of the tumor growth model with immune surveillance under cross correlated noises abstract the noise is inherent and indispensable in the tumor growth system therefore the behavior of the tumor system will display randomness different from the traditional analysis method such as the mean value variance etc the literature presents another deterministic tool i e the most probable trajectories which are defined by computing the spatial maximizers of the probability density function here we will investigate the tumor cell growth system with immune surveillance under correlated white noises from a deterministic point of view then the most probable extinction time is defined by the time when the most probable trajectories first escape to the extinction state from the tumor state afterward the probability ratio of extinction state versus tumor state characterizes treatment effects from the numerical simulation we derive that for the increasing cross correlation intensity of noises the most probable extinction time is enhanced and the therapeutic effect is weaken and conversely for the intensity of multiplicative noise in contrast there exists a critical intensity of additive noise at which the most probable extinction time is the smallest meanwhile treatment effects would be improved with the shrinking intensity of additive noise

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

permanence and positive periodic solution for the single species nonautonomous delay diffusive models abstract single species nonautonomous delay diffusion models with nonlinear growth rates are investigated some sufficient conditions are determined that guarantee the permanence of the species and the existence of a positive periodic solution which is global attractively

real number computability and domain theory we present the different constructive definitions of real number that can be found in the literature using domain theory we analyse the notion of computability that is substantiated by these definitions and we give a definition of computability for real numbers and for functions acting on them this definition of computability turns out to be equivalent to other definitions given in the literature using different methods domain theory is a useful tool to study higher order computability on real numbers an interesting connection between scott topology and the standard topologies on the real line and on the space of continuous functions on reals is stated an important result in this paper is the proof that every computable functional on real numbers is continuous w r t the compact open topology on the function space

on bendixson s criterion abstract for autonomous differential equations in r n criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories the technique is based on the study of functionals on 2 surfaces results generalize to higher dimensions a criterion of bendixson for the nonexistence of nonconstant periodic solutions in the case n 2 as an example an application to the lorenz system in r 3 is given

phase space structure and regularization of manev type problems phase space structure and regularization of manev type problems florin diacu a vasile mioc b cristina stoica c a department of mathematics and statistics university of victoria victoria canada v8w 3p4 b astronomical institute of the romanian academy astronomical observatory cluj napoca str cire silor 19 3400 cluj napoca romania c institute for gravitation and space sciences laboratory for gravitation str mendeleev 21 25 bucharest romania

pinning impulsive synchronization of reaction diffusion neural networks with time varying delays this paper investigates the exponential synchronization of reaction diffusion neural networks with time varying delays subject to dirichlet boundary conditions a novel type of pinning impulsive controllers is proposed to synchronize the reaction diffusion neural networks with time varying delays by applying the lyapunov functional method sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction diffusion neural networks with large and small delay sizes it is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network the technique used in this paper is also applicable to reaction diffusion networks with neumann boundary conditions numerical examples are presented to demonstrate the effectiveness of the theoretical results

a deterministic and stochastic model for the system dynamics of tumor immune responses to chemotherapy abstract modern medical studies show that chemotherapy can help most cancer patients especially for those diagnosed early to stabilize their disease conditions from months to years which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs in order to better understand the dynamics of tumor immune responses under chemotherapy deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper the basic dynamical properties such as boundedness existence and stability of equilibrium points are investigated in the deterministic model extended stochastic models include stochastic differential equations sdes model and continuous time markov chain ctmc model which accounts for the variability in cellular reproduction growth and death interspecific competitions and immune response to chemotherapy the ctmc model is harnessed to estimate the extinction probability of tumor cells numerical simulations are performed which confirms the obtained theoretical results

speculatively redundant continued logarithm representation continued logarithms as originally introduced by gosper represent a means for exact rational arithmetic but their application to exact real arithmetic is limited by the uniqueness of their representation this is quite unfortunate as this representation seems promising for efficient hardware implementation we propose an idea of making the representation redundant using speculative recognition of noncomputable cases this approach solves the problem of real number computability preserves most of the beneficial properties of continued logarithms and only moderately affects complexity of arithmetic algorithms thus keeping the prospect of efficient implementation

desynchronization waves in small world networks a regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased due to the spread of localized instability of eigenvectors of the laplacian matrix we find that shortcuts which make a regular network small world can destroy ordered desynchronization wave patterns wave patterns in a small world network are usually destroyed gradually as the degree of regularity in the network deteriorates no ordered wave patterns are observed in scale free and random networks the formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator we derive a general type of the kardar parisi zhang equation for phase evolution in a prototype oscillator network the equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise

synchronization transitions on scale free neuronal networks due to finite information transmission delays we investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale free neuronal networks with different average degrees and scaling exponents as the underlying model of neuronal dynamics we use the efficient rulkov map with additive noise we show that increasing the coupling strength enhances synchronization monotonously whereas delay plays a more subtle role in particular we found that depending on the inherent oscillation frequency of individual neurons regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases these delay induced synchronization transitions manifest as well expressed minima in the measure for spatial synchrony appearing at every multiple of the oscillation frequency larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization these results are robust against variations in system size intensity of additive noise and the scaling exponent of the underlying scale free topology we argue that fine tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and indeed they should be seen as important as the coupling strength or the overall density of interneuronal connections we finally discuss some biological implications of the presented results

distributed consensus for sampled data control multi agent systems with missing control inputs abstract this paper is concerned about the distributed consensus problem for general sampled data control multi agent systems without or with a leader under control inputs missing over some sampling intervals for these two cases a distributed adaptive dynamical consensus algorithm is proposed based only on the relative information of network structure under the assumption that the dynamical network contains a directed spanning tree some sufficient consensus conditions are induced under a switched model these obtained consensus criteria are independent of dynamical network topology namely they are valid for both undirected and directed topology besides they do not rely on the spectra and the eigenvalue of laplacian matrix furthermore some quantitative relations included in dynamical systems such as sampling period admissible control inputs missing rate and exponential reaching rate of the consensus performance are established finally simulation examples are given to show the effectiveness of the proposed results

cotangent bundle reduction and poincare birkhoff normal forms in this paper we study a systematic and natural construction of canonical coordinates for the reduced space of a cotangent bundle with a free lie group action the canonical coordinates enable us to compute poincare birkhoff normal forms of relative equilibria using standard algorithms the case of simple mechanical systems with symmetries is studied in detail as examples we compute poincare birkhoff normal forms for a lagrangian equilateral triangle configuration of a three body system with a morse type potential and the stretched out configuration of a double spherical pendulum

can fractional calculus help improve tumor growth models abstract ode based population models remain viable tools to investigate tumor growth and support clinical evidence by following a fractional approach this study derives analytical solutions for five of these models whose parameters are best fitted against extant clinical data in terms of tumor growth prediction results show that fractional models not only have better performance which is mostly wanted for decision making in oncology but also reveal interesting characteristics to be further explored

an investigation on monod haldane immune response based tumor effector interleukin 2 interactions with treatments abstract in this article a mathematical model with time delay describing tumor immune interaction with monod haldane kinetic response is proposed to reveal the dynamics of related inter cellular phenomena positivity of the solutions boundedness and uniform persistence of the system are determined to ensure the well posedness of the system the local stability of equilibria is studied as well as the length of the delay to preserve the stability is estimated for providing the mechanism of action to control the oscillation in tumor growth transcritical bifurcation using sotomayer s theorem and hopf bifurcation are investigated analytically and numerically global stability is examined before the commencement of sustained oscillations using a suitable lyapunov function to observe the influence of tumor growth due to uncertainty in input parameters latin hypercube sampling based uncertainty analysis is performed followed by sensitivity analysis computer simulation results are illustrated to elucidate the change of dynamical behavior due to the change of system parameters

central configurations and total collisions for quasihomogeneous n body problems abstract we consider n body problems given by potentials of the form r a r b with a b constants 0 a b to analyze the dynamics of the problem we first prove some properties related to central configurations including a generalization of moulton s theorem then we obtain several qualitative properties for collision and near collision orbits in the manev type case a 1 at the end we point out some new relationships between central configurations relative equilibria and homothetic solutions

on the dynamics of the langmuir problem we study the dynamics of an invariant set of the classical coulomb atom which generalizes the one langmuir proposed for helium in 1921 the n electrons are positioned at the vertices of a regular polygon that changes size homothetically while the nucleus moves along a line orthogonal through the centre of the polygon our main result is that for negative energy the equations of motion have infinitely many periodic solutions

stochastic bifurcation for a tumor immune system with symmetric levy noise abstract in this paper we investigate stochastic bifurcation for a tumor immune system in the presence of a symmetric non gaussian levy noise stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index the effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation we find that stochastic dynamics induced by gaussian and non gaussian levy noises are quite different

linear stability of the elliptic lagrangian triangle solutions in the three body problem abstract this paper concerns the linear stability of the well known periodic orbits of lagrange in the three body problem given any three masses there exists a family of periodic solutions for which each body is at the vertex of an equilateral triangle and travels along an elliptic kepler orbit reductions are performed to derive equations which determine the linear stability of the periodic solutions these equations depend on two parameters the eccentricity e of the orbit and the mass parameter 27 m1m2 m1m3 m2m3 m1 m2 m3 2 a combination of numerical and analytic methods is used to find the regions of stability in the e plane in particular using perturbation techniques it is rigorously proven that there are mass values where the truly elliptic orbits are linearly stable even though the circular orbits are not

stability for lagrangian relative equilibria of three point mass systems in the present paper we apply geometric methods and in particular the reduced energy momentum rem method to the analysis of stability of planar rotationally invariant relative equilibria of three point mass systems we analyse two examples in detail equilateral relative equilibria for the three body problem and isosceles triatomic molecules we discuss some open problems to which the method is applicable including roto translational motion in the full three body problem

influence of time delayed feedback in the firing pattern of thermally sensitive neurons we explore the dynamics of a hodgkin huxley type model for thermally sensitive neurons that exhibit intrinsic oscillatory activity the model is modified to include a feedback loop that is represented by two parameters the synaptic strength and the transmission delay time we analyze the dynamics of the neuron depending on the temperature the synaptic strength and the delay time we find parameter regions where the effect of the recurrent connexion is excitatory inducing spikes or trains of spikes and regions where it is inhibitory reducing or eliminating completely the spiking behavior we characterize the complex interplay of the intrinsic dynamics of the neuron with the recurrent feedback input and a noisy input

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

optimal control of drug therapy in cancer treatment abstract we present an optimal control strategy for nonlinear systems with application to the drug therapy of cancer the tumour growth model is represented by a system of equations from population dynamics which is based on the competition between normal cells and tumour cells the effect of the immune system in the presence of cancer is also included in the model a linear time varying approximation technique is proposed to construct an optimal control strategy for the nonlinear system which is valid not only within small perturbations around the equilibrium point but also for global dynamics of the system the optimal control method is applied to eliminate the tumour cells whilst minimizing the amount of drug in the simulated model simulation results show that cancer cells can be eradicated 1 in a very short time with a small amount of drug using an optimal administration of the therapy

the combined effects of optimal control in cancer remission we investigate a mathematical model depicting the nonlinear dynamics of immunogenic tumors as envisioned by kuznetsov et al 1 to understand the dynamics under what circumstances the cancer cells can be eliminated we implement the theory of optimal control we design two types of external treatment strategies one is adoptive cellular immunotherapy and another is interleukin 2 our aim is to establish the treatment regimens that maximize the effector cell count and minimize the tumor cell burden and the deleterious effects of the total amount of drugs we derive the existence of an optimal control by using the boundedness of solutions we characterize the optimality system in which the state system is coupled with co states the uniqueness of an optimal control of our problem is also analyzed finally we demonstrate the numerical illustrations that the optimal regimens reduce the tumor burden under different scenarios

exact real computer arithmetic with continued fractions a representation of the computable real numbers by continued fractions is introduced this representation deals with the subtle points of undecidable comparison and integer division as well as representing the infinite 1 0 and undefined 0 0 numbers two general algorithms for performing arithmetic operations are introduced the algebraic algorithm which computes sums and products of continued fractions as a special case basically operates in a positional manner producing one term of output for each term of input the transcendental algorithm uses a general formula of gauss to compute the continued fractions of exponentials logarithms trigonometric functions and a wide class of special functions a prototype system has been implemented in lelisp and the performance of these algorithms is promising

existence and stability of almost periodic solutions for cellular neural networks with time varying delays in leakage terms on time scales abstract this paper is concerned with cellular neural networks with time varying delays in leakage terms on time scales some sufficient conditions on the existence uniqueness and global exponential stability of almost periodic solutions are established an example is presented to illustrate the feasibility and effectiveness of the obtained results

homoclinic orbits for a class of hamiltonian systems consider the second order hamiltonian system where q n and v c 1 n is t periodic in t suppose v q t 0 0 0 is a local maximum for v t and v t x x under these and some additional technical assumptions we prove that hs has a homoclinic orbit q emanating from 0 the orbit q is obtained as the limit as k of 2 kt periodic solutions i e subharmonics q k of hs the subharmonics q k are obtained in turn via the mountain pass theorem

on the global dynamics of the anisotropic manev problem we study the global flow of the anisotropic manev problem which describes the planar motion of two bodies under the influence of an anisotropic newtonian potential with a relativistic correction term we first find all the heteroclinic orbits between equilibrium solutions then we generalize the poincare melnikov method and use it to prove the existence of infinitely many transversal homoclinic orbits invoking a variational principle and the symmetries of the system we finally detect infinitely many classes of periodic solutions

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

mathematical modeling of tumor immune competitive system considering the role of time delay abstract in this paper we consider a three dimensional nonlinear delay differential system tumor cells cytotoxic t lymphocytes t helper cells with single interaction delay we perform linear stability of the equilibria and the existence of hopf bifurcation in which the discrete time delay is used as a bifurcation parameter we estimate the length of delay to preserve the stability of period 1 limit cycle we also investigate the direction period and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory we observe that the discrete time delay plays an important role in stability switching numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay including the existence of periodic oscillations which demonstrate the phenomena of long term tumor relapse

dynamics in a tumor immune system with time delays in this paper we study the dynamical behavior of a tumor immune system t is interaction model with two discrete delays namely the immune activation delay for effector cells ecs and activation delay for helper t cells htcs by analyzing the characteristic equations we establish the stability of two equilibria tumor free equilibrium and immune control equilibrium and the existence of hopf bifurcations when two delays are used as the bifurcation parameter our results exhibit that both delays do not affect the stability of tumor free equilibrium however they are able to destabilize the immune control equilibrium and cause periodic solutions we numerically illustrate how these two delays can change the stability region of the immune control equilibrium and display the different impacts to the control of tumors the numerical simulation results show that the immune activation delay for htcs can induce heteroclinic cycles to connect the tumor free equilibrium and immune control equilibrium furthermore we observe that the immune activation delay for htcs can even stabilize the unstable immune control equilibrium

detecting and controlling unstable periodic orbits that are not part of a chaotic attractor a method for controlling unstable periodic orbits upos that have not been controllable before is presented the method is based on detecting upos that are situated outside the skeleton of a chaotic attractor the main idea is to exploit flexible parts of the attractor which under weak external perturbations allow variable excursions of the trajectory away from its originally determined path after the perturbation the trajectory of the autonomous system seeks its path back to the chaotic attractor and reveals additional upos that are otherwise not used by the system it is shown that these upos can be controlled as easily as the upos that form the basic chaotic attractor the effectiveness of the proposed method is demonstrated on two different chaotic systems with very distinct response abilities to external perturbations additionally some applications of the method in the fields of laser technology information encoding and biomedical engineering are discussed

stability and bifurcation analysis of delay induced tumor immune interaction model a modified mathematical model of kuznetsov et al 1994 representing tumor immune interaction with discrete time delay is proposed in this paper by choosing the discrete time delay as the bifurcation parameter we establish the sufficient condition for local stability of interior steady state hopf bifurcation occurs when the time delay passes a critical value the estimation of the length of delay to preserve stability has been derived moreover based on the normal form theory and center manifold theorem we establish explicit expressions to determine the direction of hopf bifurcation and the stability of bifurcating periodic solutions numerical simulations are obtained to validate our analytical findings by varying the system parameter a two parameters bifurcation diagrams are also shown by varying the system parameters which bring out the rich biological dynamics of the system

hopf bifurcation for neutral type neural network model with two delays in this paper the dynamics of a neutral neural network model with two delays is investigated the condition to ensure the stability of the zero solution of the system is decided by choosing 1 and 2 as parameters respectively then the hopf bifurcation is discussed by using the center manifold theory and normal form method introduced by hassard and kazarinoff global existence of periodic solution is studied by using the global hopf bifurcation theory finally some numerical simulations are carried out to illustrate the analytical results

correlated noise in a logistic growth model the logistic differential equation is used to analyze cancer cell population in the presence of a correlated gaussian white noise we study the steady state properties of tumor cell growth and discuss the effects of the correlated noise it is found that the degree of correlation of the noise can cause tumor cell extinction

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

the geometric minimum action method a least action principle on the space of curves freidlin wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool specifically a numerical algorithm is proposed to compute the quasi potential in the theory which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous the equilibrium distribution of the system the pathways of transition between metastable states and their rate etc can all be expressed in terms of the quasi potential we propose an algorithm to compute these quantities called the geometric minimum action method gmam which is a blend of the original minimum action method mam and the string method it is based on a reformulation of the large deviations action functional on the space of curves that allows one to easily perform the double minimization of the original action required to compute the quasi potential the theoretical background of the gmam in the context of large deviations theory is discussed in detail as well as the algorithmic aspects of the method the gmam is then illustrated on several examples a finite dimensional system displaying bistability and modeled by a nongradient stochastic ordinary differential equation an infinite dimensional analogue of this system modeled by a stochastic partial differential equation and an example of a bistable genetic switch modeled by a markov jump process

hopf bifurcation in differential equations with delay for tumor immune system competition model this paper deals with the qualitative analysis of the solutions to a model that refers to the competition between the immune system and an aggressive host such as a tumor the model which describes this competition is governed by a system of differential equations with one delay it is shown that the dynamics depends crucially on the time delay parameter by using the time delay as a parameter of bifurcation the analysis is focused on the hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state the obtained results depict the oscillations given by simulations see m galach int j appl math comput sci 13 2003 pp 395 406 which are observed in reality see d kirschner and j c panetta j math biol 37 1998 pp 235 252 it is suggested to examine by laboratory experiments how to employ these results for control of tumor growth

the global flow of the manev problem the manev problem a two body problem given by a potential of the form a r b r2 where r is the distance between particles and a b are positive constants comprises several important physical models having its roots in research done by isaac newton we provide its analytic solution then completely describe its global flow using mcgehee coordinates and topological methods and offer the physical interpretation of all solutions we prove that if the energy constant is negative the orbits are generically precessional ellipses except for a zero measure set of initial data for which they are ellipses for zero energy the orbits are precessional parabolas and for positive energy they are precessional hyperbolas in all these cases the set of initial data leading to collisions has positive measure

finiteness of polygonal relative equilibria for generalised quasi homogeneous n body problems and n body problems in spaces of constant curvature we prove for generalisations of quasi homogeneous n body problems with centre of mass zero and n body problems in spaces of negative constant gaussian curvature that if the masses and rotation are fixed there exists for every order of the masses at most one equivalence class of relative equilibria for which the point masses lie on a circle as well as that there exists for every order of the masses at most one equivalence class of relative equilibria for which all but one of the point masses lie on a circle and rotate around the remaining point mass the method of proof is a generalised version of a proof by j m cors g r hall and g e roberts on the uniqueness of co circular central configurations for power law potentials

dynamic behavior of a beddington deangelis type stage structured predator prey model abstract this paper deals with a robust stage structured predator prey model with beddington deangelis type functional response the proposed mathematical model consists of a system of three nonlinear ordinary differential equations to stimulate the interactions between prey population juvenile predators and adult predator population the positivity boundedness and the conditions for uniform persistence have been derived the dynamical behavior of the system both analytically and numerically investigated from the point of view of local stability persistence and global stability the global stability of the system has been derived by using the theory of competitive systems stability of periodic orbits and compound matrices for the interior equilibrium point depending on the conversion rate of the prey population to juvenile predator the model exhibits hopf bifurcation the model admit periodic solutions which is produced from the stage structure of the predator populations numerical simulations have been accomplished to validate our analytical findings

stochastic dynamics of michaelis menten kinetics based tumor immune interactions abstract in this paper we investigate deterministic and stochastic dynamics of michaelis menten kinetics based tumor immune interactions for the deterministic case stability analysis is performed by routh hurwitz criteria chaos is observed in bifurcation analysis and examined by the method of 0 1 test the stochastic system is constructed by incorporating multiplicative white noise terms into the deterministic system we establish a unique positive solution ensuring the positiveness and boundedness of solution from the positive initial condition the sufficient condition is obtained for weak persistence in mean we also derive the parametric restrictions for stochastic permanence and global attractivity in mean finally we validate the extinction of tumor cells with the transition from co existence domain by crossing the estimated threshold values of intensity of environmental noise

near collision dynamics for particle systems with quasihomogeneous potentials abstract we study collision and ejection orbits of 3 particle systems having the potential w u v where u and v are homogeneous functions of degree a and b respectively with 1 a b we show that for b 2 collision and ejection orbits tend to form asymptotically a central configuration for the case b 2 which corresponds to maneff s gravitational law we find a set of collision and ejection orbits reaching the triple collision manifold without asymptotic phase this set contains an uncountable union of manifolds and has positive measure within the set of all rectilinear solutions

global asymptotic stability of stochastic bam neural networks with distributed delays and reaction diffusion terms this paper is concerned with global asymptotic stability of a class of reaction diffusion stochastic bi directional associative memory bam neural networks with discrete and distributed delays based on suitable assumptions we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for reaction diffusion stochastic bam neural networks with discrete and distributed delays the obtained results are easy to check and improve upon the existing stability results an example is also given to demonstrate the effectiveness of the obtained results

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

fear factor in a prey predator system in deterministic and stochastic environment abstract in this article a prey predator model has been studied where apart from direct predation the prey population is affected by the fear induced from predators the basic reproduction of the prey population is reduced as a cost of fear biologically well posedness of the model system has been shown through positivity and boundedness of solutions existence criterion and stability analysis of the non negative equilibrium points have been discussed and necessary conditions for uniform persistence have been derived for corresponding non autonomous system also sufficient conditions for the existence of positive periodic solution of the non autonomous system have been established by utilizing the coincidence degree theorem we further show that the positive periodic solution is global attractor under certain conditions next we construct the stochastic model based upon the deterministic setup by perturbing the intrinsic growth rate of prey and natural mortality rate of predators it has been shown that the stochastic system admits unique positive global solution initiates from anywhere in the interior of the positive quadrant the sufficient conditions for extinction non persistence and weakly persistence of both the species have been derived along with the stochastic permanence of the system we have verified our analytical results and make a comparison between the deterministic and stochastic setup by exhaustive numerical simulations

stability of synchronous oscillations in a system of hodgkin huxley neurons with delayed diffusive and pulsed coupling we study the synchronization dynamics for a system of two hodgkin huxley hh neurons coupled diffusively or through pulselike interactions by calculating the maximum transverse lyapunov exponent we found that with diffusive coupling there are three regions in the parameter space corresponding to qualitatively distinct behaviors of the coupled dynamics in particular the two neurons can synchronize in two regions and desynchronize in the third when excitatory and inhibitory pulse coupling is considered we found that synchronized dynamics becomes more difficult to achieve in the sense that the parameter regions where the synchronous state is stable are smaller numerical simulations of the coupled system are presented to validate these results the stability of a network of coupled hh neurons is then analyzed and the stability regions in the parameter space are exactly obtained

stochastic resonance in a tumor immune system subject to bounded noises and time delay abstract immunotherapy is one of the most recent approaches in cancer therapy a mathematical model of tumor immune interaction subject to a periodic immunotherapy treatment imitated by a periodic signal correlative and bounded stochastic fluctuations and time delays is investigated by numerical simulations for its signal power amplification spa within the tailored parameter regime the synchronous response of tumor growth to the immunotherapy stochastic resonance sr versus both the noises and delays is obtained the details are as follows i the peak values of spa versus the noise intensity a in the proliferation term of tumor cells decrease as the frequency of periodic signal increases i e an increase of the frequency restrains the sr ii an increase of the amplitude of periodic signal restrains the sr versus a but boosts up the sr versus the noise intensity b in the immune term iii there is an optimum cross correlated degree between the two bounded noises at which the system exhibits the strongest sr versus the delay time the reaction time of tumor cell population to their surrounding environment constraints iv upon increasing the delay time double sr versus the delay time the time taken by both the tumor antigen identification and tumor stimulated proliferation of effectors emerges these results may be helpful for an immunotherapy treatment for the sufferer

extreme fluctuations in stochastic network coordination with time delays we study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks we obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network we then obtain the scaling behavior of the extreme fluctuations with system size as well as the distribution of the extremes on complex networks and compare them to those on regular one dimensional lattices for large complex networks when the delay is not too close to the critical one fluctuations at the nodes effectively decouple and the limit distributions converge to the fisher tippett gumbel density in contrast fluctuations in low dimensional spatial graphs are strongly correlated and the limit distribution of the extremes is the airy density finally we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes

a remark on the ode with two discrete delays abstract the aim of this paper is to outline a formal framework for the analytical analysis of the hopf bifurcations in the delay differential equations with two independent time delays some results for the differential difference equations with two delays when the both of the coefficients of linearized equation are negative were obtained in x li s ruan j wei stability and bifurcation in delay differential equations with two delays j math anal appl 236 1999 254 280 in the paper we present some remarks on the case studied in x li s ruan j wei stability and bifurcation in delay differential equations with two delays j math anal appl 236 1999 254 280 and also two other cases namely when the coefficients of linearized equation have different signs and when coefficients are both positive

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

the impact of the media awareness and optimal strategy on the prevalence of tuberculosis abstract in this present study we propose and analyze a mathematical model of tuberculosis tb transmission considering social awareness effects during an epidemic possible equilibrium points of the model are investigated and their stability criterion is discussed basic reproduction number r0 of the model is obtained through the next generation matrix method it has been shown that the infection free equilibrium is locally stable when r0 1 the global asymptotic stability of the endemic equilibrium p is verified by constructing a suitable lyapunov function the possibility of two endemic equilibria when r0 r 0 1 also verified using center manifold theory the media awareness parameters influence the occurrence of backward bifurcation an optimal control problem is framed considering a media intervention parameter u t as a control variable the existence and characterization of the optimal solution to the problem solved analytically optimal media control strategy with accessible media intervention cost gradually reduce the prevalence of the disease in addition to our analytical results several numerical simulations are also performed to make the analysis more significant a short discussion on the media guided transmission characteristic of the disease obtained from our investigation is conducted at last

synchronization transition in scale free networks clusters of synchrony we study the synchronization transition in scale free networks that display power law asymptotic behaviors in their degree distributions the critical coupling strength and the order parameter critical exponent derived by the mean field approach depend on the degree exponent ensuremath lambda which implies a close connection between structural organization and the emergence of dynamical order in complex systems we also derive the finite size scaling behavior of the order parameter finding that the giant cluster of synchronized nodes is formed in different ways between scale free networks with 2l ensuremath lambda l3 and those with ensuremath lambda g3

a time delay model of tumour immune system interactions global dynamics parameter estimation sensitivity analysis abstract recently a large number of mathematical models that are described by delay differential equations ddes have appeared in the life sciences in this paper we present a delay differential model to describe the interactions between the effector and tumour cells the existence of the possible steady states and their local stability and change of stability via hopf bifurcation are theoretically and numerically investigated parameter estimation problem for given real observations using least squares approach is studied the global stability and sensitivity analysis are also numerically proved for the model the stability and periodicity of the solutions may depend on the time lag parameter the model is qualitatively consistent with the experimental observations of immune induced tumour dormancy the model also predicts dormancy as a transient period of growth which necessarily results in either tumour elimination or tumour escape

switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation one dimensional models are important for developing demonstrating and testing new methods and approaches which can be extended to more complex systems we design for a linear delay differential equation a reliable numerical method which consists of two time splits as follows a it is an exact scheme at the early time evolution t where is the discrete value of the delay b thereafter it is a nonstandard finite difference nsfd scheme obtained by suitable discretizations at the backtrack points it is shown theoretically and computationally that the nsfd scheme is dynamically consistent with respect to the asymptotic stability of the trivial equilibrium solution of the continuous model extension of the nsfd to nonlinear epidemiological models and its good performance are tested on a numerical example

real functions incrementally computable by finite automata this is an investigation into exact real number computation using the incremental approach of potts ph d thesis department of computing imperial college 1998 edalat and potts electronic notes in computer science vol 6 elsevier science publishers amsterdam 2000 nielsen and kornerup j universal comput sci 1 7 1995 527 and vuillemin ieee trans on comput 39 8 1990 1087 where numbers are represented as infinite streams of digits each of which is a mobius transformation the objective is to determine for each particular system of digits which functions r r can be computed by a finite transducer and ultimately to search for the most finitely expressible mobius representations of real numbers the main result is that locally such functions are either not continuously differentiable or equal to some mobius transformation this is proved using elementary properties of finite transition graphs and mobius transformations applying the results to the standard signed digit representations we can classify functions that are finitely computable in such a representation and are continuously differentiable everywhere except for finitely many points they are exactly those functions whose graph is a fractured line connecting finitely many points with rational coordinates

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

paths to globally generalized synchronization in scale free networks we apply the auxiliary system approach to study paths to globally generalized synchronization in scale free networks of identical chaotic oscillators including h enon maps logistic maps and lorentz oscillators as the coupling strength ensuremath epsilon between nodes of the network is increased transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds are found the generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of ensuremath epsilon our result is useful for understanding the synchronization process in complex networks

existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi homogeneous n body problems and the curved n body problem we prove that if for relative equilibrium solutions of a generalisation of quasi homogeneous n body problems the masses and rotation are given then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero we furthermore prove that the set of such relative equilibria is compact and prove related results for n body problems in spaces of constant gaussian curvature

pcf extended with real numbers we extend the programming language pcf with a type for total and partial real numbers by a partial real number we mean an element of a cpo of intervals whose subspace of maximal elements single point intervals is homeomorphic to the euclidean real line we show that partial real numbers can be considered as continuous words concatenation of continuous words corresponds to refinement of partial information the usual basic operations cons head and tail used to explicitly or recursively define functions on words generalize to partial real numbers we use this fact to give an operational semantics to the above referred extension of pcf we prove that the operational semantics is sound and complete with respect to the denotational semantics a program of real number type evaluates to a head normal form iff its value is different from b if its value is different from b then it successively evaluates to head normal forms giving better and better partial results converging to its value author s abstract

synchronization processes in complex networks we present an extended analysis based on the dynamics towards synchronization of a system of coupled oscillators of the hierarchy of communities in complex networks in the synchronization process different structures corresponding to well defined communities of nodes appear in a hierarchical way the analysis also provides a useful connection between synchronization dynamics complex networks topology and spectral graph analysis

the control gain region for synchronization in non diffusively coupled complex networks abstract the control gain region for synchronization of non diffusively coupled networks was studied with respect to three conditions synchronization synchronization in finite time and synchronization in the minimum time based on cancellation control methodology and master stability function formalism we found that a complete feasible control gain region may be bounded unbounded empty or a union of several bounded and unbounded regions with a similar shape to the synchronized region an interesting possibility emerged that a network could be synchronized by both negative and positive feedback control simultaneously by bridging synchronizability and synchronizing response speeds with a settling time index we have developed timed synchronized region tsr as a substitute for the classical synchronized region to study finite time synchronization as for the last condition a graphical method was developed to estimate control gain with the minimum synchronization time cgmst each condition has examples provided for illustration and verification

stochastic model for tumor growth with immunization we analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero cross correlations in between whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise moreover the system is subjected to an external additive noise which mimics the influence of the environment of the tumor the stationary probability distribution p s is derived depending on the finite correlation time the immunization rate and the strength of the cross correlation p s offers a maximum which becomes more pronounced for increasing immunization rate the mean first passage time is also calculated in order to find out under which conditions the tumor can suffer extinction its characteristics are again controlled by the degree of immunization and the strength of the cross correlation the behavior observed can be interpreted in terms of a biological model of tumor evolution

synchronization of oscillators through time shifted common inputs shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems however due to finite signal transmission speeds and differences in the distance to the source time shifts between otherwise common inputs are unavoidable since common inputs can be a source of correlation between the elements of multi unit dynamical systems regardless of whether these elements are directly connected with one another or not it is of importance to understand their impact on synchronization as a canonical model that is representative for a variety of different dynamical systems we study limit cycle oscillators that are driven by stochastic time shifted common inputs we show that if the oscillators are coupled time shifts in stochastic common inputs do not simply shift the distribution of the phase differences but rather the distribution actually changes as a result the best synchronization is therefore achieved at a precise intermediate value of the time shift which is due to a resonance like effect with the most probable phase difference that is determined by the deterministic dynamics

synchronization transition in degenerate optical parametric oscillators induced by nonlinear coupling in this paper the synchronization of certain degenerate optical parametric oscillators is investigated in detail complete and or partial synchronization can be reached when linear controller constructed by the real part or imaginary part of the subharmonic mode is imposed on the chaotic degenerate optical parametric oscillators with appropriate coupling intensity the lyapunov exponents under different coupling coefficients are calculated to find the critical condition for complete synchronization transition from complete synchronization to partial synchronization is observed when nonlinear coupling is introduced into the two chaotic oscillators it is found that synchronization of chaotic oscillators keeps robust when the intensity of the nonlinear coupling is less than the intensity of the linear coupling the complete synchronization state is destructed and transient period for partial synchronization is in certain delay when the intensity of the nonlinear coupling is beyond the intensity of the linear coupling