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We consider regular lattices of coupled chaotic maps whose local dynamics is ruled by the logistic map x ↦ 4 x ( 1 − x ) , a usual paradigm of chaotic systems. Through finite-time exponents, we scrutinize the lattice dynamics in the vicinity of the threshold of complete synchronization. We connect dynamical features such as relaxation to the coherent state and intermittency with the statistics of finite-time exponents, focusing on the implications of the particular statistics related to the logistic map. Although numerical examples are given for lattice couplings decaying with distance as a power law, our results are expected to be valid for a wider class of schemes coupling logistic maps.

Spatially extended dynamical systems subjected to a periodic external input are able to store short-term memories as a result of self-organization. This phenomenon has been used to interpret sliding charge density wave experiments, and has been found in lattices of coupled maps and oscillators. In this paper, we aim to describe the influence of a stochastic perturbation in the self-organized memories in a lattice of coupled linear and weakly nonlinear maps. We consider the case in which the coupling between maps depends on the lattice distance as a power law.

We investigate aspects of the spatio-temporal dynamics exhibited by a one-dimensional lattice of chaotic piecewise linear maps in a coupling prescription which includes both regular (nearest and next-to-nearest neighbors) and randomly chosen couplings. We discuss the conditions for the existence of chaotic synchronized states, and relate them to the coupling parameters. The transition to synchronized behavior is described, and we explore some statistical properties of the time it takes to achieve this regime.

Spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales, characterized by repeated conversions from spatially localized transient chaos into global laminar patterns. A simple model, yet retaining some features of more complex systems, consists of a lattice of a class of tent maps with an escaping region. The coupling prescription we adopt in this work considers the interaction of a site with all its neighbors, the corresponding strength decaying with the lattice distance as a power-law. This makes possible to pass continuously from a local (nearest-neighbor) to a global kind of coupling. We investigate statistical properties of both the chaotic transient bursts and the periodic laminar states, with respect to the coupling parameters.

Analytical tokamak plasma equilibria, with non-monotonic plasma current profile and perturbed by ergodic magnetic limiters, are described by non-twist conservative maps. Examples are given of concentration of magnetic field lines escaping to the tokamak wall. The robustness of invariant curves on the shearless region is also observed.

Tuned liquid column dampers are U-tubes filled with some liquid, acting as an active vibration damper in structures of engineering interest like buildings and bridges. We study the effect of a tuned liquid column damper in a vibrating system consisting of a cart which vibrates under driving by a source with limited power supply (non-ideal excitation). The effect of a liquid damper is studied in some dynamical regimes characterized by coexistence of both periodic and chaotic motion.

We investigate some dynamical effects of adding a certain amount of noise in a theoretical model for rattling in single-stage gearbox systems with a backlash, consisting of two wheels with a sinusoidal driving. The parameter intervals we are dealing with show an extremely involved attraction basin structure in phase space. One of the observable effects of noise is basin hopping, or the switching between basins of different attractors. We characterize this effect and its relation to the presence of chaotic transients.

The ergodic magnetic limiter is a device designed to generate a cold boundary layer of chaotic magnetic field lines at the peripheral region of a tokamak, with the main purpose of reducing the deleterious effects of the plasma–wall interaction. In the TCABR tokamak an ergodic limiter was constructed and recently installed inside the vacuum chamber. We developed a theoretical model for the action of an ergodic magnetic limiter in a large aspect-ratio tokamak taking into account the finite width of the limiter. The theoretical results are in good agreement with measurements of the vacuum magnetic field created by the limiter. Poincare maps of field line flow are computed to reveal the resulting magnetic field line structure due to the ergodic limiter and show that the operation of the ergodic limiter in the TCABR tokamak is feasible and results in a chaotic boundary layer for limiter currents of about 6% of the plasma current.

Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on–off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents.

We investigate short-term memories in linear and weakly nonlinear coupled map lattices with a periodic external input. We use locally coupled maps to present numerical results about short-term memory formation adding a stochastic perturbation in the maps and in the external input.

We claim that dynamical traps displayed by chaotic orbits of non-integrable Hamiltonian systems can be characterized using properties of the finite-time Lyapunov exponent. We show that, for the case where the phase space presents stickiness regions, the distribution of the finite-time Lyapunov exponent is bimodal, while, for the case where no such regions exist, the distribution is a Gaussian-like one.

Transport barriers have been observed in tokamak experiments involving negative magnetic shear. The use of non-twist maps has been proposed in order to explain the underlying dynamical mechanism of such barriers. In this work we derive an area-preserving analytical map to describe the formation of a transport barrier in a chaotic field line region of a tokamak with an ergodic magnetic limiter. The map so obtained is used to investigate the radial diffusion of field lines in such a configuration.

We investigate numerically the dynamical behavior of a non-ideal mechanical system consisting of a vibrating cart containing a particle which can oscillate back and forth colliding with walls carved in the cart. This system represents an impact damper for controlling high-amplitude vibrations and chaotic motion. The motion of the cart is induced by an in-board non-ideal motor driving an unbalanced rotor. We study the phase space of the cart and the bouncing particle, in particular the intertwined smooth and fractal basin boundary structure. The control of the chaotic motion of the cart due to the particle impacts is also investigated. Our numerical results suggests that impact dampers of small masses are effective to suppress chaos, but they also increase the final-state sensitivity of the system in its phase space.

The structure of magnetic field lines in a tokamak with reversed magnetic shear is investigated by means of analytically derived area-preserving non-twist Poincare maps. The basic configuration is the magnetic field produced by an ergodic limiter, superimposed to the tokamak equilibrium field in suitable coordinates. We consider the cases of one and two resonant modes, focusing on magnetic island dimerization and the formation of a transport barrier in the chaotic layer of field lines.

We used numerical diagnostics to quantify spatial disorder, and its relation with temporal chaos, for a one-dimensional chain of coupled logistic maps with a coupling strength which varies with the lattice distance in a power-law fashion. The main tool is spatial return plots, whose properties are used to obtain information about the chaotic synchronized states of the system. A spatial correlation integral is introduced to characterize the clustering of points in the spatial return plots.

We examine the existence of an invariant manifold in the phase space structure presented by a dissipative four-wave coupling. We show that, once in such manifold, the system preserves two quantities as time evolves: a quantity related to the energy of the system and another, related to the exchange of energy between the waves. We observe that the presence of this manifold allows the system to manifest stable solutions for a specific interval of the dissipation parameters. Out of this range the system brings up only uncoupled states (no nonlinear saturated states). The dissipation parameters affect only the transversal dynamics to the manifold, changing how quickly the invariant manifold is reached. In the invariant manifold, the system exhibits a large number of coexisting periodic attractors—limit cycles (coupled states), with an interwoven structure of basins of attraction. The time series of conserved quantities and the properties of the Lyapunov spectra are used to imply the existence of a lower-dimensional invariant manifold. Since the dynamics in such invariant manifold preserves an energy-like function, we identify it as being conservative.

We investigated the structure of magnetic field lines in a tokamak with reversed magnetic shear and non-symmetric perturbations by means of analytically derived area-preserving non-twist Poincare maps. The maps are used to study magnetic island dimerization and the formation of a transport barrier in the chaotic layer of field lines.

We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations.

We investigate a phenomenological model for the heartbeat consisting of two coupled Van der Pol oscillators. The coupling between these nodes can be both unidirectional or bidirectional, and an external driving produced by a pacemaker is also included in this model. In order to warrant a robust operation, it is desirable that both units oscillate in a synchronized way, even though in the presence of external in0uences or parameter mismatches which are unavoidable in a physiological setting. We study the synchronization properties of such an association with respect to the nature andintensity of coupling. We analyze in particular the (generalized ) synchronization of rhythms characterizedby a chaotic mod ulation of the oscillator frequencies. We also investigate the shadowing breakdown of numerically generated chaotic trajectories of the coupled oscillator system via unstable dimension variability in its chaotic invariant set. c

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving. The equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure.

Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents.

Reversed magnetic shear configurations in tokamaks reduce substantially particle diffusivity and improve plasma confinement due to the formation of a transport barrier, as a result of magnetic field line reconnection and bifurcation. The latter are caused by the resonant perturbation of an ergodic limiter on a tokamak with reversed magnetic shear, which creates a region with chaotic field lines in the vicinity of the dimerized island chains. An analytically derived nontwist map for field lines is used to describe the formation of a transport barrier, manifested in the decrease of field line diffusion rate. This barrier appears due to the chaotic field line trapping near the reconnection layer that survives the bifurcation.

The time evolution of the lowest order transversal oscillation mode of a suspension bridge is studied by means of a piecewise-linear forced and damped one-dimensional oscillator, in which the loss of smoothness is due to the asymmetric response of the bridge hangers with respect to stretching and compression. If the midpoint roadbed deflection is outside a specified safe region, the bridge is supposed to collapse. We analyze the relative area of the safe basin, or the fraction of initial conditions in the phase space for which the bridge does not collapse with respect to the damping and forcing parameters. The safe basin erosion is enhanced by the appearance of incursive fingers caused by the exponential accumulation of safe basin lobes towards an invariant manifold of a periodic orbit which undergoes a homoclinic bifurcation.

We investigate the emergence of mode locking, or frequency synchronization, in a chain of coupled sine-circle maps with randomly distributed parameters, and exhibiting the small-world property. The coupling prescription we adopt considers the nearest and next-to-the-nearest neighbors of a given site, as well as randomly chosen non-local shortcuts, according to a given probability. A transition between synchronized and non-synchronized patterns is observed as this probability is varied. We also study the statistics of the synchronization plateaus, evidencing a Poisson-type distribution.

Electric power systems are frequently nonlinear and, when faced with increasing power demands, may behave in unpredictable and rather irregular ways. We investigated the nonlinear dynamics of a single machine infinite bus power system model in order to study the appearance of coexistent periodic and chaotic attractors, characterizing multi-stable behavior. The corresponding basins of attraction present fractal boundaries, for which we have determined the uncertain fraction scaling in phase space. The bifurcation diagrams are studied with respect to variations of the mechanical power input and may lead to voltage collapse under certain circumstances, which we relate to a boundary crisis suffered by a chaotic attractor.

We consider a symplectic map for magnetic field lines in a tokamak with an ergodic limiter, whose function is to generate a perturbing magnetic field which causes the formation of chaotic field lines in the vicinity of the tokamak inner wall. We analyze numerically the onset of global chaos due to the interaction of adjacent magnetic islands, the size of the chaotic region, and investigate anomalous diffusion and loss of field lines due to their collisions with the tokamak wall.

We consider the single mode dynamics of a self-pulsating semiconductor laser model under modulated injection current. The observation of a chaotic regime for a wide range of parameters suggests the usefulness of this model for high-speed secure optical communications. A possible way to achieve symbol encoding by using such a laser as a light source is to control its chaotic dynamics. We study the stabilization of periodic orbits embedded in the chaotic invariant set of the system by applying perturbations on the amplitude of the injection current.

The action of a set of ergodic magnetic limiters in tokamaks is investigated from the Hamiltonian chaotic scattering point of view. Special attention is paid to the influence of invariant sets, such as stable and unstable manifolds, as well as the strange saddle, on the formation of the chaotic layer at the plasma edge. The nonuniform escape process associated to chaotic field lines is also analyzed. It is shown that the ergodic layer produced by the limiters has not only a fractal structure, but it possesses the even more restrictive Wada property.

We propose a Hamiltonian formulation to study the magnetic field line structure in a tokamak with ergodic magnetic limiter. An analytical stroboscopic mapping, derived from this formulation, is used to investigate the onset of global field line chaos at the plasma edge and the Hamiltonian bifurcations of magnetic axes.

We present analytical results for the Kolmogorov–Sinai entropy of a one-dimensional lattice of locally coupled piecewise linear maps, for some particular values of the coupling strength. Our results explain the numerically observed fact that the entropy of a lattice of chaotic maps increases for strong coupling.

The dynamics of a negative gain suppression factor laser diode subjectedto injection current modulation is similar to that of a damped nonlinearoscillator under periodic forcing. Quasi-periodicity, frequency lockingand chaos may be present, depending on the values of the forcingparameters. We have found, for some parameter values, type-Iintermittent behavior and crisis-induced intermittency. Scaling lawswere obtained for the duration of the laminar phase and the chaos-chaosswitchings, respectively. The scale exponents are very close to thoseexpected for one-dimensional unimodal maps.

Short-term memory formation is a collective e-ect displayed by driven spatiotemporal dynamical systems, in which the injectedsignal is echoedback in many d ways d to the coupling e-ect. The existence of multiple short-term memories enables us to use these systems to encode signals. We present numerical evidence of short-term memory generation in a lattice of AC-driven circuits with inductive coupling. The multiple con4gurations exhibited by this oscillator chain can be usedto encod e graphical characters. c 2002 Elsevier Science B.V. All rights reserved.

In recent years, it became clear that a better understanding of the interactions among the main elements involved in the cancer network is necessary for the treatment of cancer and the suppression of cancer growth. In this work we propose a system of coupled differential equations that model brain tumour under treatment by chemotherapy, which considers interactions among the glial cells, the glioma, the neurons, and the chemotherapeutic agents. We study the conditions for the glioma growth to be eliminated, and identify values of the parameters for which the inhibition of the glioma growth is obtained with a minimal loss of healthy cells.

We considered a clustered network of bursting neurons described by the Huber-Braun model. In the upper level of the network we used the connectivity matrix of the cat cerebral cortex network, and in the lower level each cortex area (or cluster) is modelled as a small-world network. There are two different coupling strengths related to inter- and intracluster dynamics. Each bursting cycle is composed of a quiescent period followed by a rapid chaotic sequence of spikes, and we defined a geometric phase which enables us to investigate the onset of synchronized bursting, as the state in which the neuron start bursting at the same time, whereas their spikes may remain uncorrelated. The bursting synchronization of a clustered network has been investigated using an order parameter and the average field of the network in order to identify regimes in which each cluster may display synchronized behavior, whereas the overall network does not. We introduce quantifiers to evaluate the relative contribution of each cluster in the partial synchronized behavior of the whole network. Our main finding is that we typically observe in the clustered network not a complete phase synchronized regime but instead a complex pattern of partial phase synchronization in which different cortical areas may be internally synchronized at distinct phase values, hence they are not externally synchronized, unless the coupling strengths are too large.

Master–slave systems have been intensively investigated for modelling the application of chaos in communications. We considered Colpitts oscillators coupled according to a master–slave configuration in order to study chaos synchronization. We revealed the existence of superpersistent transients in this coupled system. The transient is a ubiquitous phenomenon in nonlinear dynamical systems, and it is responsible for important physical phenomena. We characterized superpersistent transients through a scaling law for their average lifetime. Unstable–unstable pair bifurcation has been identified as the generic mechanism for these transients. Moreover, we showed that an additive noise, added to the slave system, may suppress the chaos synchronization. Our results show that synchronization can be achieved for higher coupling strength when there is noise. However, the noise may induce a longer transient if the synchronization is not suppressed.

Riddling occurs in dissipative dynamical systems with more than one attractor, when the basin of one attractor is punctured with holes belonging to the basins of the other attractors. The basin of a chaotic attractor is riddled if (i) it has a positive Lebesgue measure; (ii) in the vicinity of every point belonging to the basin of the attractor, there is a positive Lebesgue measure set of points that asymptote to another attractor. We investigate the presence of riddled basins in a two-dimensional noninvertible map with a symmetry-breaking term. In the symmetric case the onset of riddling is characterized by an unstable–unstable pair bifurcation, which also leads to unstable dimension variability in the invariant chaotic set. The nonsymmetric case exhibits a chaotic attractor, but a riddled basin occurs only at the bifurcation point, since after that the attractor becomes a chaotic saddle. We analyze the presence of unstable dimension variability in the symmetric case by computing the finite-time transverse Lyapunov exponents. We point out some consequences of those facts to the synchronization properties of coupled chaotic systems.

We consider a lattice of coupled chaotic logistic maps in which the coupling strength between sites decreases with the lattice distance in a power-law fashion, making possible to pass continuously from a local to a global coupling. The corresponding Lyapunov spectra are described by means of the maximal exponent and the average of the positive exponents, which are analyzed in terms of the coupling properties. Our results are compared with spatio-temporal patterns known for global and local couplings.

A numerical study of chaotic field line diffusion in a tokamak with an ergodic magnetic limiter is described. The equilibrium model field is analytically obtained by solving a Grad–Schluter–Shafranov equation in toroidal polar coordinates, and the limiter field is determined by supposing its action as a sequence of delta-function pulses. A symplectic twist mapping is introduced to analyze the mean square radial deviation of a bunch of field lines in a predominantly chaotic region. The formation of a stochastic layer and field diffusivity at the plasma edge are investigated. Field line transport is initially subdiffusive and becomes superdiffusive after a few iterations. The field lines are lost when they collide with the tokamak inner wall; their decay rate is exponential with Poisson statistics.

We consider the stationary magnetohydrodynamical (MHD) equilibrium equation for an axisymmetric plasma undergoing azimuthal rotations. The case of cylindrical symmetry is treated, and we present two semi-analytical solutions for the stationary MHD equilibrium equations, from which a number of physical properties of the magnetically confined plasma are derived.

We consider the effects of external nonsymmetric magnetostatic perturbations caused by resonant helical windings and a chaotic magnetic limiter on the plasma confined in a tokamak. The main purpose of both types of perturbation is to create a region in which field lines are chaotic in the Lagrangian sense: two initially nearby field lines diverge exponentially through many turns around the tokamak. The equilibrium field is obtained from the equations of magneto-hydrodynamic equilibrium written down in a polar toroidal coordinate system. The magnetic fields generated by the resonant helical windings and the chaotic magnetic limiter are obtained through an analytical solution of Laplace equation. The magnetic field line equations are integrated to give a Hamiltonian mapping of field lines that we use to characterize the structure of chaotic field lines. In the case of resonant windings, we obtained the map by both numerical integration and a Hamiltonian formulation. For a chaotic limiter, we analytically derived a symplectic map by using a Hamiltonian formulation.

An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension variability is a cause of severe modeling difficulty for physical phenomena, since trajectories obtained from the mathematical model may not be related to trajectories of the actual system. We present and example of unstable dimension variability occurring in a system of two coupled chaotic maps, considering the dynamics in the synchronization manifold and its corresponding transversal direction, where a tongue-like structure is formed. The unstable dimension variability is revealed in the statistical distribution of the finite-time transversal Lyapunov exponent, having both negative and positive values., Comment: 25 pages, 8 figures, RevTex format

Frequency synchronization is a common phenomenon in spatially extended dynamical systems, like oscillator chains and coupled map lattices. We study the distribution of synchronization plateaus in a sine-circle map lattice with a variable range coupling and randomly distributed natural frequencies. A transition between synchronized and nonsynchronized phases is observed as the coupling range is varied. The lengths of the synchronization plateaus are found to obey an exponential distribution for local coupling.

The stationary equilibrium of an axisymmetric plasma characterized by toroidal and poloidal flows is considered within the framework of ideal double adiabatic magnetohydrodynamic equations. The problem is reduced to a nonlinear partial differential equation for the poloidal magnetic flux function, containing six surface functions, plus a nonlinear algebraic Bernoulli equation defining the plasma density. Ellipticity conditions and bifurcations of its solutions are discussed in the limit of small beta, appropriated for tokamak-like equilibria. Possible connections with the L-H transition are suggested.

A class of kicked nonlinear limit cycle oscillators is described by a prototype circle map. We consider a spatially extended system in which these maps are coupled in a unidimensional lattice, according to a coupling scheme that includes the global (mean-field) and local (nearest-neighbor) prescriptions as limiting cases. We analyze frequency synchronization in the system, investigating its behavior under variations of the coupling parameters.

We derive, according to a procedure introducedby Maschke and Perrin, an equation for MHD stationaryequilibrium with azimuthal rotation in an orthogonalcurvilinear coordinate system. We assume that there is an ignorable coordinate so that surfacequantities like the magnetic flux and the rotationfrequency do not depend on it. The temperature is alsoconsidered a surface quantity. As an application of the formalism, we consider prolate spheroidalcoordinates, which are convenient for studying plasmarotation in compact tori configurations likeSpheromaks.

In this work, we analyze the transition from regular to chaotic states in the parametric four-wave interactions. The temporal evolution describing the coupling of two sets of three-waves with quadratic nonlinearity is considered. This system is shown to undergo a chaotic transition via the separatrix chaos scenario, where a soliton-like solution (separatrix) that is found for the integrable (perfect matched) case becomes irregular as a small mismatch is turned on. As the mismatch is increased the separatrix chaotic layer spreads along the phase space, eventually engrossing most part of it. This scenario is typical of low-dimensional Hamiltonian systems.

We estimate the threshold value of the perturbation strength needed to cause magnetic field-line stochasticity in the peripheral region of a Tokamak zvith an ergodic magnetic limiter, accoriding to a Hamiltonian description for field lines. We model the limiter action as a periodic sequence of impulsive excitations. Two global stochasticity prescriptions are used: Chirikov's overlapping criterion and the renormalization scheme of Escande, Doveil and Benkadda.

An equation for stationary MHD equilibrium with azimuthal rotation in spherical coordinates is derived. Following a procedure introduced by Maschke and Perrin, by supposing that the plasma temperature is a surface quantity, we describe a two-parameter family of axisymmetric toroidal configurations. The equilibrium equation is analytically solved for given hypotheses in such a way as to investigate the effect of plasma rotation on the magnetic field structure.

As redes funcionais do cerebro saoo compostas por areas corticais que estao anatomicamente e funcionalmente conectadas. Analises estatisticas sugerem que a estrutura cerebral pode ser descrita atraves de uma estrutura de rede de redes, onde cada rede apresenta uma topologia livre de escala com hubs densamente conectados. Construimos uma uma rede de redes livres de escala inspirada no cortex cerebral do gato para, assim, estudar suas propriedades dinâmicas. Focamos na sincronizacao dos disparos neurais das areas corticais e em como suprimir esse efeito por meio da desativacao de um neuronio atraves de pulsos de luz. Mostramos que e possivel suprimir a sincronizacao dos disparos perturbando apenas um unico hub, pois este e altamente conectado e, portanto, possui grande influencia sobre a rede.

Uma das possiveis formas de conter o crescimento de um tumor e a infusao de substâncias quimicas que afetam o funcionamento celular. Esse processo e conhecido como quimioterapia, e consiste em um tratamento que utiliza de uma forma geral, combinacoes de drogas aplicadas por meio de protocolos m´medicos. Neste trabalho propoe-se modelar interacoes do sistema imunologico, tumores e efeitos da quimioterapia por meio de equacoes diferenciais. Para tanto, estudou-se o modelo proposto por Banerjee e Sarkar, adicionando-se ao mesmo termos que representam a quimioterapia. No desenvolvimento do trabalho, apresentam-se analises da aplicacao de quimioterapia na forma continua e na forma periodica. Com o modelo proposto observou-se a supressao do câncer aplicando-se quimioterapia continuamente, sem a eliminacao de linfocitos e obteve-se protocolos de quimioterapia que maximizam a eliminacao das celulas cancerigenas enquanto minimizam os efeitos negativos nas celulas normais.