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Bifurcation of limit cycles from separatrix cycles and centers of planar perturbed analytic systems, based on the theory that there is a link between the number, multiplicities and positions of limit cycles and those of the zeros of the Melnikov function for the system, reveals new results. Changes in the qualitative behavior of a planar analytic system characterizes bifurcation.

As power systems become more heavily loaded, there will be an increase in the number of situations where the power flow equations have no real solution, particularly in contingency analysis and planning applications. Since these cases can represent the most severe threats to viable system operation, it is important that a computationally efficient technique be developed to both quantify the degree of unsolvability, and to provide optimal recommendations of the parameters to change to return to a solvable solution. Such an algorithm is developed in the paper. The distance in parameter space between the desired operating point and the closest solvable operating point provides a measure of the degree of unsolvability, with the difference between these two points providing the optimal system parameter changes. The algorithm is based upon a Newton-Raphson power flow algorithm, which provides both computational efficiency and compatibility with existing security analysis techniques. The method is demonstrated on systems of up to 118 buses.

An I-V phase space using sophisticated logging systems helps study the change of state in stationary metal contacts under the influence of high current densities and within a 50-Hz applied current cycle. Results indicate the instability in the mechanically contacted metals. Area disturbances due to surface deformation, material evaporation and condensation, and the presence of MIM microcontacts injecting charges through tunnelling, field emission and ionization beyond 0.1 MV/cm may cause the unstable behavior in the metal contacts.

A ring cavity system consisting of two hybrid Michelson interferometers coupled together with feedback is constructed. This system shows spatial bifurcation and can be utilized as an all-optical flip-flop device. We demonstrate experimentally a flip-flop operation by use of only a positive pulse in this system.

The harmonic balance approach is used to analyze tangent (saddle-node) and flip (period-doubling) bifurcations of limit cycles in periodically forced nonlinear dynamical systems. An algebraic system of equations, whose unknowns are the coefficients of a truncated Fourier series, is defined and the relationships between the bifurcations of the solutions of this algebraic system and the tangent and flip bifurcations of the limit cycles are pointed out. Some examples are presented to illustrate the method and its accuracy.

Bifurcations occurring in power system models exhibiting voltage collapse have been the subject of several recent studies. Although such models have been shown to admit a variety of bifurcation phenomena, the view that voltage collapse is triggered by possibly the simplest of these, namely by the (static) saddle node bifurcation of the nominal equilibrium, has been the dominant one. The authors have recently shown that voltage collapse can occur 'prior' to the saddle node bifurcation. In the present paper, a new dynamical mechanism for voltage collapse is determined: the boundary crisis of a strange attractor or synonymously a chaotic blue sky bifurcation. This determination is reached for an example power system model akin to one studied in several recent papers. More generally, blue sky bifurcations (not necessarily chaotic) are identified as important mechanisms deserving further consideration in the study of voltage collapse.

Chua's double scroll is probably the best known and most extensively studied example of chaotic behaviour generated by electrical circuits. It is illustrated in this paper that by modifying the characteristic of the nonlinear resistor with additional break points even more 'complicated' attractors can be obtained, called n-double scrolls (n=1,2,3,4,...). The new circuit can be seen as a generalization of Chua's circuit such that the 1-double scroll corresponds to the classical double scroll. The construction of the attractors was partially based on a combination of linearization around equilibrium points and an alternative method for studying nonlinear systems that we called a quasilinear approach. This method is heuristic and qualitative but may give additional global insight into the state space behaviour and may open new views towards the construction of attractors.

A strange attractor has been found in a system described by a differential-difference equation: a delayed cellular neural network composed by only two cells; a detailed analysis of the set of eigenvalues that give rise to the attractor is presented and the bifurcation phenomena obtained by varying the delay are shown.

The Afraimovich-Shilnikov theorem on 2-D torus breakdown is formulated and used to carry out a detailed numerical investigation of the bifurcation routes from the torus to chaos in a third-order torus circuit. Three scenarios of transition to chaos due to torus breakdown take place in this circuit in complete agreement with the theorem: 1) Period-doubling bifurcations of the phase-locked limit cycles 2) saddle-node bifurcation in the presence of a homoclinic structure 3) soft transition due to the loss of torus smoothness.

Suarez and Duffy have noted an interesting bifurcation in a two-level gridpoint general circulation model when strong tropical heating is imposed. This bifurcation results in a model climatology with strong upper-level westerlies in the tropics. In this paper, it is argued that this bifurcation is essentially due to the dominant role played by extratropical baroclinic transients in the tropical angular momentum budget. A series of numerical experiments is analyzed with a global two-level primitive equation model, using spectral truncation in the horizontal. The model climatologies in these experiments fall into two categories: 1) conventional, that is, weak upper-level easterlies/westerlies in the tropics; and 2) superrotating, that is, strong upper-level westerlies in the tropics. An attempt is made to explain the maintenance of the general circulation in these two radically different climatologies by studying the properties of unstable normal modes for the two different time-mean states. The spectral characteristics of angular momentum transport due to transient eddies in these two climatologies are also discussed. To understand the meridional propagation of transient eddies, the notion of a 'modal' refractive index in the quasigeostrophic approximation is introduced. From this analysis it is concluded that the conventional climatology is stable to weak perturbations, with the 'restoring' force being provided primarily by extratropical baroclinic eddies. Strong perturbations completely change the propagation characteristics of these eddies, leading to a bifurcation of the general circulation. This has interesting implications for the range of validity of two-level models and the transitivity of tropospheric general circulation.

The equilibrium positions of a partially submerged rod supported at one end are considered. Simple examples of bifurcations occur, and the breaking of these bifurcations by an 'imperfection' is discussed.

This paper describes the implementation of both Point of Collapse (PoC) methods and continuation methods for the computation of voltage collapse points (saddle-node bifurcations) in large ac/dc systems. A comparison of the performance of these methods is presented for real systems of up to 2158 buses. The paper discusses computational details of the implementation of the PoC and continuation methods, and the unique challenges encountered due to the presence of high voltage direct current (HVDC) transmission, area interchange power control, regulating transformers, and voltage and reactive power limits. The characteristics of a robust PoC power flow program are presented, and its application to detection and solution of voltage stability problems is demonstrated.

A proposed approach for obtaining self-consistent solutions for field and rate equations is presented for the study of frequency locking, quasi-periodicity, subharmonic bifurcations and chaos. Results show that gain-guided stripe-geometry semiconductor lasers are derived in high-frequency modulation current by the dynamic and modulation signals. Chaos or quasiperiodic vibrations are generated with synchronized modulation signals and periodic outputs.

A branch-switching strategy in an elastostatic bifurcation problem is described. Only linearized incremental equations are used. Higher-order terms of increments and eigenvalue analysis are not required. Uneconomical iteration during random access to the secondary path can be avoided. Near the bifurcation point, the loading parameter is fixed to define a constant-loading plane that intersects the equilibrium branches. All these intersections are stationary points of potential energy located closely in the vicinity of bifurcation point. A trajectory passing through these intersections is introduced at the assumed loading level. Line search with a termination criterion will be initiated to detect a stationary point of potential energy in the tangent direction of the curve. Iteration is then started from this detected stationary point to attain a regular point on the postbifurcation path. In a complex branching situation, line search in the improved tangent direction or tracing of the trajectory is recommended. Asymmetric bifurcation and multi-branching of the frame and truss are treated in numerical examples. Clustered bifurcation, too, is computed.

A mapping is derived in closed form, without approximations, for an idealized current-mode controlled boost converter. This circuit is known experimentally to behave chaotically for certain values of the reference current, and to produce subharmonics of the clock frequency at others. Numerical iteration of the mapping indicates chaotic operation and the presence of subharmonics. Two mechanisms of bifurcation are explained.

Properties of discontinuous bifurcation solutions for elastic-plastic solids are established for conventional test conditions that are pertinent to experiments on soil, powder, and rock. Typically, such conditions are characterized as plane strain and axisymmetry. A restricted form of nonassociativity is assumed, where only the volumetric portion of the flow rule is nonassociated. Apart from this restriction, the aim is to make as general predictions as possible without resorting to a specific elastic-plastic model. It is shown that states of plane strain are far more susceptible to bifurcations than those encountered in the conventional triaxial apparatus (which represents cylindrical stress states). Moreover, the solutions for dilatant materials will rarely bifurcate under conventional triaxial compression (CTC) test conditions, while conventional triaxial extension (CTE) test conditions fall between the two extremes of plane strain and CTC. For Drucker-Prager criterion it is shown that bifurcation is never possible in the hardening regime for CTC. These findings are in agreement with experimentally observed behavior when it can be ensured that the stress state is sufficiently homogeneous throughout the specimen., The plastic bifurcation for plane strain versus axisymmetry for granular materials is examined. The granular materials such as soil or rock show cohesion and frictional strength. The materials may also dilate or contract depending on the internal characteristics and direction of loading path. In the plane strain state, the materials exhibit bifurcation and in the axisymmetric state, there are restrictions for this condition in the hardening regime.

This letter introduces a new method for obtaining the maximum loading point (MLP) of electric power systems based on the load flow method with optimal multiplier in rectangular coordinates. The proposed method starts from an infeasible point beyond power system maximum loadability and approaches the MLP iteratively. Tests on several IEEE test systems and a real system show its effectiveness. Index Terms--Limit-induced bifurcation, maximum loading point, optimal multiplier, saddle-node bifurcation, static voltage stability.

Double-diffusive convection (D.D.C.) is a nonlinear fluid-dynamical phenomenon, driven by thermal and compositional effects on the density. We discuss the nature of subcritical, finite-amplitude, double-diffusive convection for infinite Prandtl number and large Lewis number, Le, which have applications in magma chambers and at the D'-layer at the core-mantle boundary (CMB). Numerical solutions by two-dimensional, finite-element method are presented to portray the nature of time-dependent D.D.C. in both the diffusive and the finger regimes. The compositional heterogeneities at the CMB are far more complex than the local thermal structure because of the large Le and may have important implications for the scattering of seismic waves off the CMB. The effects of increasing the buoyancy ratio [R.sub.[rho]] are to suppress time-dependent D.D.C. even at high Ra. In narrow slots shear-heating instabilities can be triggered in the finger regime by the abrupt overturn of the compositional interface. This phenomenon may occur in tall magma chambers with low dissipation numbers of of order 0 (0.01).

A new formulation of the Ostwald supersaturation-nucleation-depletion cycle is adopted to model precipitate banding in rocks. In a special limiting case, the system is shown to support a propagating steady deposition pulse. The limit of existence is determined analytically for a simple model analogue of a pyrite/goethite system. Using numerical simulations, an unsteady pulse of mineral deposition is obtained and is shown to develop a variety of patterns with an appropriate change in the system parameters--apparently showing that the steady pulse obtained analytically is unstable. The domains of existence of unsteady pulse, undulatory patterns and discrete bands are determined.

Painting the Phase Space Portrait of an Integrable Dynamical System SEVERAL DEVELOPMENTS UNDERLIE the present revival in classical mechanics, including computerized algebraic processors and color graphics. Dynamical processes are very [...]

Research into uniform solutions of Landau-Lifshitz-Gilbert equation linked with magnetostatic Maxwell equations is presented. It was possible to identify the complete phase portrait and bifurcation diagram of thin films with negligible crystal anisotropy.

The complex dynamics of the chaotic neural networks makes it possible for them to escape from local minimum of the simple gradient descent neurodynamics. In this letter we use a transiently chaotic neural network to detect the CDMA multiuser signals and hence obtain an implementation scheme of the CDMA multiuser detector (TCNN-MD). Computer simulation results show that the proposed detector is clearly superior to Hopfield neural-network-based detector. Index Terms - Bifurcation, multiuser detection, transiently chaotic neural network.

This note presents a fast stability test algorithm for two-dimensional (2-D) systems which requires max {O([m.sup.2]), O([mn.sup.2] [log.sub.2] mn), O([mn.sup.4])} multiplications to test the stability of [Mathematical Expression Omitted].

A Fourier-transformed Fokker-Planck transport equation was used to characterize the time evolution of the spin distribution for the XY model in mean-field theory using a fully dynamical-systems approach. The results showed that regardless of the initial spin distribution, all point attractors determined the equilibrium state of the model. Phase transition at the critical temperature was accompanied by a supercritical bifurcation.

This paper reports experimental results with a real circuit, which realizes the chaotic lady's shoe attractor with a two-cell cellular neural network (CNN). The experiments show very interesting bifurcation phenomena, and in certain parameter region the circuit becomes chaotic according to the on-line measured Poincare map and power spectrum, which confirms the existence of the lady's shoe attractor discovered in computer simulations (3).

The short-wave instability due to Horpf bifurcation in a reaction-diffusion model of glycolytic oscillations is investigated. Very low values of the ration d of the diffusion coefficient of the inhibitor and that of the activator (ADP) do help to create short waves, whereas high values of the ratio d and the complexing reaction of the activator ADP reduces drastically the wave-instability domain, generating much longer wavelengths.

The present study performed three sets of idealized laboratory experiments with the aim of investigating the importance on the bifurcation mechanism of the obstacle's horizontal cross sectional geometry, the influence of the height of the obstacle, and the importance of the slope of the obstacle sidewalls. The results of the study suggest that bifurcation of a self-propagating cyclonic vortex interacting with an obstacle occurs only when the obstacle height is equal or larger than 85% of the total water depth.

This paper describes the bifurcation phenomena of a system of parallel-connected dc/dc buck converters. The results provide useful information for the design of stable current sharing in a master--slave configuration. Computer simulations are performed to capture the effects of variation of some chosen parameters on the qualitative behavior of the system. These are summarized in a series of bifurcation diagrams. In particular, it is found that while variation of the voltage feedback gains leads to standard period-doubling bifurcation, variation of the current sharing ratio leads to border collision bifurcation. Analysis is presented to establish the possibility of the bifurcation phenomena and to locate the current sharing ratio at which border collision occurs. Index Terms--Bifurcation, buck converter, parallel dc-dc converter.

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the [Delta] plane. The method exploits some quadratic and linear properties of the load flow equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem. Index Terms--Bifurcation, load flow analysis, power systems.

An autonomous free-running Cuk converter is studied in this paper. Analysis of the describing nonlinear state equations shows that the system loses stability via a supercritical Hopf bifurcation. The boundary of stability is derived and local trajectories of motion studied. Cycle-by-cycle simulations of the actual system reveal the typical bifurcation from a stable equilibrium state to chaos, via limit cycles, and quasi-periodic orbits. Experimental measurements confirm the bifurcation scenarios. The occurrence of such kinds of bifurcation in autonomous dc/dc converters has been rarely known in power electronics. Index Terms--Bifurcation, chaos, Cuk converter, dc/dc converter, power electronics.

For the first time, an exhaustive linear and nonlinear stability analysis of multitransistors monolithic-microwave integrated-circuit (MMIC) circuits is presented. A key point of the proposed stability analysis lies in that it can be easily implemented on any computer-aided design (CAD) software. The presented approach allows both linear and nonlinear stability analysis of any complex circuit fed by small or large signals. Two examples are given that demonstrate the accuracy of the method. The first example concerns a MMIC heterojunction-bipolar-transistor power amplifier, which exhibited division frequency phenomena and spurious oscillations that were detected by simulations and confirmed by measurements. The second example deals with a voltage-controlled oscillator and demonstrates that the method can also predict spurious oscillations in autonomous circuits. Index Terms--Bifurcation, characteristic determinant, conversion matrix, eigenvalues, harmonic balance, normalized determinant function, Nyquist locus, return ratio.

The Instability Principle or Harrod's knife-edge instability states that the warranted rate of growth is a unique moving equilibrium which is highly unstable. Over time, economist Roy Harrod changed the interpretation of his theory in which a concept similar to the corridor stability was introduced. Knife-edge instability under the assumptions of price-flexibility and putty-clay technology in the goods market yielded results that were consistent with Harrod's later pronouncements.

The physical mechanism of the forcing of the deep flow in the absence of interfacial friction was investigated within a quasi-geostrophic two-layer model. The investigation focused on the first Hopf bifurcation in which the steady flow changes to time-dependent behavior and compared the time mean of the trajectory with the unstable steady state offered by the continuation approach. It is observed that nonlinear self-interactions of this unstable oscillatory mode induce the rectification of the lower-layer flow.

The solution for bifurcation of orthotropic solids presented in a study made a basic error because it ignored the primary prebuckling displacements. The prebuckling displacements are equally important as the prebuckling stresses at the buckling state. The inclusion of these terms is suggested to provide a rigorous analysis procedure. The equation to obtain the derivatives of the prebuckling displacements using the constitutive equation for this orthotropic half space are provided.

In this paper, we study the deformation and stability of a planar elastica. One end of the elastica is clamped and fixed in space. The other end of the elastica is also clamped, but the clamp itself is allowed to slide along a linear track with a slope different from that of the fixed clamp. The elastica deforms after it is subjected to an external pushing force on the moving clamp. It is observed that when the pushing force reaches a critical value, snapping may occur as the elastica jumps from one configuration to another remotely away from the original one. In the theoretical investigation, we calculate the static load-deflection curve for a specified slope difference between the fixed clamp and the moving clamp. To study the stability of the equilibrium configuration, we superpose the equilibrium configuration with a small perturbation and calculate the natural frequencies of the deformed elastica. An experimental setup is designed to measure the load-deflection curve and the natural frequencies of the elastica. The measured load-deflection relation agrees with the theoretical prediction very well On the other hand, the measured natural frequencies do not agree very well with the theoretical prediction, unless the mass of the moving clamp is taken into account.

The adverse health effects of inhaled particulate matter from the environment depend on its dispersion, transport, and deposition in the human airways. Similarly, precise targeting of deposition sites by pulmonary drug delivery systems also relies on characterizing the dispersion and transport of therapeutic aerosols in the respiratory tract. A variety of mechanisms may contribute to convective dispersion in the lung; simple axial streaming, augmented dispersion, and steady streaming are investigated in this effort. Flow visualization of a bolus during inhalation and exhalation, and dispersion measurements were conducted during steady flow in a three-generational, anatomically accurate in vitro model of the conducting airways to support this goal. Control variables included Reynolds number, flow direction, generation, and branch. Experiments illustrate transport patterns in the lumen cross section and map their relation to dispersion metrics. These results indicate that simple axial streaming, rather than augmented dispersion, is the dominant steady convective dispersion mechanism in symmetric Weibel generations 7-13 during normal respiration. Experimental evidence supports the branching nature of the airways as a possible contributor to steady streaming in the lung. [DOI: 10.1115/1.2838042] Keywords: respiratory airway, bifurcation, secondary flow, aerosol transport, dispersion, drug delivery

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches. [DOI: 10.111511.2838041] Keywords: mass transfer coefficient, bifurcation, single path, lungs, CFD, airways, expiration

The author examines a 1982 theorem that implies that only period doubling bifurcations happen in families of interval maps. He provides a simpler proof than the original mathematicians and a corollary.

This paper reports a methodological approach to the analysis and design of sinusoidal oscillators based on bifurcation analysis. The simple Colpitts oscillator is taken as an example to demonstrate this nonlinear approach for both the nearly sinusoidal and chaotic modes of operation. In particular, it is shown how regular and irregular (chaotic) oscillations can be generated, depending on the circuit parameters. Index Terms - Bifurcations, chaos, coexistence of solutions, Colpitts oscillator, continuation methods.

Research was conducted to examine the generation of a 20-GHz gain-switched pulse by using a high-speed multiple-quantum-well laser. An irregular behavior that included chaos and period-doubling in a gain-switched solitary laser operated at 20 GHz was observed. A rate-equation analysis using parameters extracted from small-signal response characteristics showed that the irregularity was caused by a high modulation frequency and small gain compression factor of the laser used in the experiment.