Intermittency Route Research Articles

Dynamic Behaviors of a Fractional Order Viscoelastic Two-Member Truss

The fractional dynamics equation of a viscoelastic two-member truss system, in which fractional derivative model introduced to simulate the materials’ characteristics, is proposed. The simplified single DOF differential equation is developed combined with boundary conditions and symmetry. Dynamic behaviors of the fractional single DOF system with harmonic loads are discussed by numerical calculations. The results show that: the system may lead to chaotic motion via period-doubling bifurcations or intermittent routes; the dynamical character is greatly inflected by the varying of excitation amplitude or damping coefficient or fractional order.

Intravenous therapy: preparation and administration of IV medicines

The aim of this article is to review the preparation and administration of intravenous (IV) therapy and to outline safe standards of practice. This article reviews the preparation for the procedure and then outlines actions for preparing--the patient, the practitioner, the environment and equipment, and then the medication--before describing the administration of any IV medication, whether via a bolus, intermittent or continuous route. A review of errors in IV therapy indicated calculation skill and a wide knowledge is required, while the National Patient Safety Agency (NPSA) (2010) highlighted omited and delayed medications as the second largest cause of medication incidents. Therefore the Royal College of Nursing (RCN) (2010) suggested each practitioner must have knowledge of the principles of reconstituting, including aseptic technique, compatibility (physical, chemical, and therapeutic), stability, storage, labelling, interactions, dosage, calculations and the use of appropriate equipment. Furthermore, Finlay (2004) advocated that training must also include the management of anaphylaxis. The necessity for safe and consistent IV practice is endosed and explored through Crimlisk et al's (2009) nine rights of IV medications, and Billings and Kowalski's (2005) mnemonic (CATS:PRRR).

Intravenous therapy: preparation and administration of IV medicines

The aim of this article is to review the preparation and administration of intravenous (IV) therapy and to outline safe standards of practice. This article reviews the preparation for the procedure and then outlines actions for preparing—the patient, the practitioner, the environment and equipment, and then the medication—before describing the administration of any IV medication, whether via a bolus, intermittent or continuous route. A review of errors in IV therapy indicated calculation skill and a wide knowledge is required, while the National Patient Safety Agency (NPSA) (2010) highlighted omitted and delayed medications as the second largest cause of medication incidents. Therefore, the Royal College of Nursing (RCN) (2010) suggested each practitioner must have knowledge of the principles of reconstituting, including aseptic technique, compatibility (physical, chemical and therapeutic), stability, storage, labelling, interactions, dosage, calculations and the use of appropriate equipment. Furthermore, Finlay (2004) advocated that training must also include the management of anaphylaxis. The necessity for safe and consistent IV practice is endorsed and explored through Crimlisk et al's (2009) nine rights of IV medications, and Billings and Kowalski's (2005) mnemonic (CATS:PRRR).

Exposure to chronic intermittent nicotine vapor induces nicotine dependence

Animal models of drug exposure are important tools for the study of the neurobiological mechanisms of nicotine dependence and as preclinical models for medication development. There are few non-invasive animal models of nicotine exposure and currently there is no known animal model of second-hand exposure to nicotine. We hypothesized that chronic administration of nicotine vapors would produce blood levels of nicotine in rodents that are clinically relevant to those observed in human smoking and that rodents exposed to nicotine vapors would develop dependence to nicotine. We developed a system that vaporizes nicotine in the air in a stable, reliable and consistent manner. Intermittent exposure to nicotine vapor (0.2 mg/m 3) for 8 or 14 h per day for 7 days produced a concentration of nicotine in the blood of 22 ng/mL. Sixteen hours after removal from nicotine vapors, rats showed significant somatic withdrawal signs precipitated by mecamylamine (1.5 mg/kg). These results provide a new rodent model of nicotine dependence using vapor administration that produces consistent levels of nicotine in the blood that are relevant for both heavy smoking and second-hand smoking, using a non-invasive technique that mimics the intermittent aspect and route of administration in humans.

Intermittency route to strange nonchaotic attractors in a non-skew-product map

Whether strange nonchaotic attractors (SNAs) can typically arise in non-skew-product maps has been a crucial question for more than two decades. Recently, it was shown that SNAs arise in a particular non-skew-product map related to quasiperiodically driven continuous dynamical systems [R. Badard, Chaos, Solitons Fractals 28, 1327 (2006); Chaos 18, 023127 (2008)]. In the present paper, we derive Badard's non-skew-product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigate onset mechanisms of SNAs in the map. In particular, we focus on a transition route to intermittent SNAs, where SNAs appear after pair annihilations of stable and unstable fixed points located on a ring-shaped invariant curve. Then the mean residence time and rotation numbers have a logarithmic singularity. Finally, we discuss the existence of SNAs in a special class of non-skew-product maps.

Intermittency in amplitude modulated dynamic atomic force microscopy

From a mathematical point of view, the atomic force microscope (AFM) belongs to a special class of continuous time dynamical systems with intermittent impact collisions. Discontinuities of the velocity result from the collisions of the tip with the surface. Transition to chaos in non-linear systems can occur via the following four routes: bifurcation cascade, crisis, quasi-periodicity, and intermittency. For the AFM period doubling and period-adding cascades are well established. Other routes into chaos, however, also may play an important role. Time series data of a dynamic AFM experiment indicates a chaotic mode that is related to the intermittency route into chaos. The observed intermittency is characterized as a type III intermittency. Understanding the dynamics of the system will help improve the overall system performance by keeping the operation parameters of dynamic AFM in a range, where chaos can be avoided or at least controlled.

On–off intermittent synchronization between two bidirectionally coupled double scroll circuits

In this report the intermittent route from full synchronization to full desynchronization, of two bidirectionally coupled, double-scroll circuits, was experimentally studied. Coupling resistance, between the two circuits, served as the bifurcation parameter, controlling the synchronization. It was shown that the synchronization–desynchronization transition was realized through a regime of incomplete synchronization of the on–off intermittency type.

CLASSIFICATION OF BIFURCATIONS AND CHAOS IN CHUA'S CIRCUIT WITH EFFECT OF DIFFERENT PERIODIC FORCES

We study the effect of different periodic excitations like sine, square, triangle and sawtooth waves on Chua's circuit and show that the circuit can undergo distinctly modified bifurcation structure, generation of new periodic regimes, induction of crises and so on. In particular, we point out that under the influence of different periodic excitations, a rich variety of bifurcation phenomena, including the familiar period-doubling sequence, intermittent route to chaos and period-adding sequences, reverse bifurcations, remerging chaotic band attractors, a large number of coexisting periodic attractors exist in the system. The analysis is carried out numerically using phase portraits, two-parameter phase diagrams in the forcing amplitude-frequency plane and one-parameter bifurcation diagrams. The chaotic dynamics of this circuit is also realized experimentally.

Experimental investigation on chaotic behaviors in loss-modulated erbium-doped fiber-ring lasers

Chaotic behaviors in loss-modulated erbium-doped fiber-ring lasers are reported. In a single-frequency loss-modulated erbium-doped fiber-ring laser, the coexistence of period-doubling bifurcation and intermittency routes to chaos is observed by changing the modulation frequency or the modulation voltage. The results are in agreement with those in an erbium-doped fiber-ring laser subjected to pump modulation. Dual-frequency loss-modulated erbium-doped fiber-ring lasers are proposed. When the value of the frequency ratio is approximately equal to the gold mean and the silver mean, respectively, the transition to chaos via quasiperiodicity is found when the modulation voltage is increased. The modulation voltages for the transition are different for the varied values of the frequency ratio.

The effects of variations in dose and method of administration on glucagon like peptide-2 activity in the rat

Glucagon-like peptide-2 (GLP-2) is a potent, intestinal-specific trophic hormone. However, the relationship between the dose and timing of GLP-2 administration and these trophic effects is not clear. We investigated the effects of variations in the dose and timing of GLP-2 administration on its intestinal trophic activity. A rodent model of total parenteral nutrition (TPN) mucosal atrophy was used, examining intestinal morphology in the adult male rat after 5 days. Groups were: controls, maintained with TPN alone and GLP-2 treated groups (high dose; 240 μg/kg/day, low dose; 24 μg/kg/day) given by continuous or intermittent (over 1 h, twice daily) intravenous infusion. Body weight and total small bowel length were significantly increased in the high dose, continuous infusion group. Both high dose infusion methods increased total small bowel weight, villus height, crypt depth, and total mucosal surface area. Both high dose infusion and low dose intermittent infusion routes increased crypt cell proliferation ( P < 0.05 for all comparisons). Both high dose routes gave nearly equivalent exposures; low dose continuous infusion gave higher exposure but intermittent low dose infusion resulted in an increase in crypt proliferation; neither low dose method resulted in morphologic changes. There were no differences in transporter protein expression or apoptosis rates. High dose continuous infusion appears to maximally induce intestinal growth, and also increases weight gain, while high dose GLP-2 intermittent infusion results in similar morphologic effects. A threshold level for the induction of proliferative and morphologic effects was seen in the low dose groups. These observations may be relevant for planning therapeutic trials.

THE INTERMITTENCY ROUTE TO CHAOS OF AN ELECTRONIC DIGITAL OSCILLATOR

An electronic oscillator producing digital signals, formed by a second-order, nonlinear, nonautonomous, closed loop topology that is based on two integrators and nonlinear elements (a comparator and a XOR gate), was experimentally investigated. For a certain frequency and amplitude range of the periodic driving signal, the intermittency route to chaos was observed and studied.

Continuous PGE 2 leads to net bone loss while intermittent PGE 2 leads to net bone gain in lumbar vertebral bodies of adult female rats

The present study examined the effects of continuous and intermittent PGE 2 administration on the cancellous and cortical bone of lumbar vertebral bodies (LVB) in female rats. Six-month-old Sprague–Dawley female rats were divided into 6 groups with 2 control groups and 1 or 3 mg PGE 2/kg given either continuously or intermittently for 21 days. Histomorphometric analyses were performed on the cancellous and cortical bone of the fourth and fifth LVBs. Continuous PGE 2 exposure led to bone catabolism while intermittent administration led to bone anabolism. Both routes of administration stimulated bone remodeling, but the continuous PGE 2 stimulated more than the intermittent route to expose more basic multicellular units (BMUs) to the negative bone balance. The continuous PGE 2 caused cancellous bone loss by stimulating bone resorption greater than formation (i.e., negative bone balance) and shortening the formation period. It caused more cortical bone loss than gain, the magnitude of the negative endocortical bone balance and increased intracortical porosity bone loss was greater than for periosteal bone gain. The anabolic effects of intermittent PGE 2 resulted from cancellous bone gain by positive bone balance from stimulated bone formation and shortened resorption period; while cortical bone gain occurred from endocortical bone gain exceeding the decrease in periosteal bone and increased intracortical bone loss. Lastly, a scheme to take advantage of the marked PGE 2 stimulation of lumbar periosteal apposition in strengthening bone by converting it to an anabolic agent was proposed.

Intermittency transition to generalized synchronization in coupled time-delay systems

We report the nature of the transition to generalized synchronization (GS) in a system of two coupled scalar piecewise linear time-delay systems using the auxiliary system approach. We demonstrate that the transition to GS occurs via an on-off intermittency route and that it also exhibits characteristically distinct behaviors for different coupling configurations. In particular, the intermittency transition occurs in a rather broad range of coupling strength for the error feedback coupling configuration and in a narrow range of coupling strength for the direct feedback coupling configuration. It is also shown that the intermittent dynamics displays periodic bursts of periods equal to the delay time of the response system in the former case, while they occur in random time intervals of finite duration in the latter case. The robustness of these transitions with system parameters and delay times has also been studied for both linear and nonlinear coupling configurations. The results are corroborated analytically by suitable stability conditions for asymptotically stable synchronized states and numerically by the probability of synchronization and by the transition of sub-Lyapunov exponents of the coupled time-delay systems. We have also indicated the reason behind these distinct transitions by referring to the unstable periodic orbit theory of intermittency synchronization in low-dimensional systems.

APERIODIC NONCHAOTIC ATTRACTORS, STRANGE AND OTHERWISE

The main conceptual issues in the study of strange nonchaotic dynamics have been summarized and reviewed earlier [Prasad et al., 2001]. In the past five years, there has been further progress in the analysis of such attractors, and in understanding the nature of dynamical transitions in quasiperiodically forced systems. Here we discuss new developments which include the creation of strange nonchaotic attractors in excitable systems, the elucidation of the mechanisms for the intermittent and fractalization routes to SNA as well as their potential applications. The possibility of creating such attractors without recourse to quasiperiodic forcing is an important objective, and this has been realized in specific circumstances.

Nonlinear flow of wormlike micellar gels: Regular and chaotic time-dependence of stress, normal force and nematic ordering

We present our recent experiments on the nonlinear dynamics in the flow behaviour of shear-thinning wormlike micellar gels. In particular, we have shown experimentally that above a critical shear rate, the initial transient stress response comprises of overshoots and undershoots and this is followed by periodic, quasiperiodic, intermittent and chaotic behaviour. The normal force dynamics is similar to that of the stress. This can be classified as Type-II intermittency route to chaos. In our system, shear-thinning wormlike micellar solution of cetyltrimethylammonium tosylate, the strength of flow–concentration coupling is tuned by the addition of salt sodium chloride. The existence of a “butterfly” intensity pattern in small angle light scattering (SALS) performed simultaneously with the rheological measurements confirms the coupling of flow to concentration fluctuations in the system under study. Dynamic light scattering measurements to extract the relaxation time scales of concentration fluctuations are in excellent agreement with the in situ SALS measurements performed under shear. The scattered depolarised intensity in SALS, sensitive to orientational order fluctuations, shows the same time-dependence (like intermittency) as that of shear stress at various wave vectors.

Mode-to-mode energy transfers in convective patterns

We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.

Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force

The homoclinic bifurcation and transition from regular to asymptotic chaos in Duffing oscillator subjected to an amplitude modulated force is studied both analytically and numerically. Applying the Melnikov analytical method, the threshold condition for the occurrence of horseshoe chaos is obtained. Melnikov threshold curves are drawn in different external parameters space. Analytical predictions are demonstrated through direct numerical simulations. Parametric regimes where suppression of horseshoe chaos occurs are predicted. Period doubling route to chaos, intermittency route to chaos and quasiperiodic route to chaos are found to occur due to the amplitude-modulated force. Numerical investigations including computation of stable and unstable manifolds of saddle, maximal Lyapunov exponent, Poincaré map and bifurcation diagrams are used to detect homoclinic bifurcation and chaos.

Tuning Rheochaos by Temperature in Wormlike Micelles

We investigate the critical role played by the mean micellar length during the route to rheochaos for wormlike micellar gels of surfactant cetyltrimethylammonium tosylate in the presence of salt sodium chloride that show coupling of flow to concentration fluctuations. To this end, we have carried out stress/shear rate relaxation experiments at a fixed shear rate/stress but at different temperatures to take the sample through the route to rheochaos. We see the type-II intermittency route to rheochaos in stress relaxation measurements and the type-III intermittency route to rheochaos in shear rate relaxation measurements. We have also carried out linear rheology measurements at different temperatures to estimate the mean micellar length (-)L, the reptation time tau(rep), and the breaking time tau(break). It is shown that (-)L changes by approximately 58%, as the sample goes through the route to rheochaos.

Nonlinear dynamics and chaos in a fractional-order financial system

This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found.

Routes to chaos, universality and glass formation

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis’ q-exponential functions. Furthermore, the addition of a noise perturbation to the dynamics at the onset of chaos of the logistic map allows to establish parallels with the behavior of supercooled liquids close to glass formation. Specifically, the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest is corroborated for such a system.