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Abstract: We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model. [Copyright &y& Elsevier]

Abstract In this study, we investigate a discrete-time version of logit dynamics, as applied to the rock–paper–scissors (RPS) game. First, we show that around the Nash equilibrium point, an attracting closed invariant curve appears due to the Neimark–Sacker bifurcation. Next, near the resonance point, we find a period-three attracting cycle, which can be thought of as a counterpart to the cyclically stable set in the RPS game with best response dynamics. Moreover, we show that the cycle can coexist with an attracting closed invariant curve, a period-three saddle cycle, and the attracting or repelling Nash equilibrium point. Finally, we use the codimension-two bifurcation theory to specify the set of heteroclinic bifurcations that destroy the coexistence of the attractors. Highlights • The rock–paper–scissors game in discrete-time logit dynamics is analyzed. • An attracting closed invariant curve around the Nash equilibrium appears. • The coexistence of period three cycles and attracting Nash equilibrium is proved. • The coexistence of period three cycles and closed invariant curve is proved. • Heteroclinic cycle of RPS game in discrete-time logit dynamics is conjectured. [ABSTRACT FROM AUTHOR]

Abstract: The game ‘rock–paper–scissors’ model, with the consideration of the effect of the psychology of conformity, is investigated. The interaction between each two agents is global, but the strategy of the conformity is local for individuals. In the statistical opinion, the probability of the appearance of each strategy is uniform. The dynamical analysis of this model indicates that the equilibrium state may lose its stability at a threshold and is replaced by a globally oscillating state. The global oscillation is induced by the local conformity, which is originated from the synchronization of individual strategies. [Copyright &y& Elsevier]

In this paper, we prove the existence of nontrivial contractible domains Ω ⊂ S d , d ≥ 2 , such that the overdetermined elliptic problem { − ε Δ g u + u − u p = 0 in Ω, u > 0 in Ω, u = 0 on ∂Ω, ∂ ν u = constant on ∂Ω, admits a positive solution. Here Δ g is the Laplace-Beltrami operator in the unit sphere S d with respect to the canonical round metric g , ε > 0 is a small real parameter and 1 < p < d + 2 d − 2 (p > 1 if d = 2). These domains are perturbations of S d ∖ D , where D is a small geodesic ball. This shows in particular that Serrin's theorem for overdetermined problems in the Euclidean space cannot be generalized to the sphere even for contractible domains. [ABSTRACT FROM AUTHOR]

• A novel full nonlinear mathematical model of asymmetric hydro turbine governing system established. • The multi-stability characteristics of as well as its generation mechanism are revealed. • The effect mechanism of water diversion system topology on the system stability is revealed. • The recommended setting values of system parameters under different topologies are provided. This paper aims to study the stability and nonlinear dynamics of hydro-turbine governing system with asymmetric water diversion system, i.e. asymmetric hydro turbine governing system, by using Hopf bifurcation theory. Firstly, the full nonlinear mathematical model of asymmetric hydro turbine governing system is established by all system components and nonlinear head loss. This model contains two units with different capacities which share a common pipeline. Based on the nonlinear mathematical model, the multi-stability characteristics of asymmetric hydro turbine governing system under load disturbance is studied by using stable domain and verified by numerical simulation. Moreover, the multi-time scale oscillation is revealed and its relationship to system multi-stability is investigated. Furthermore, the effect of system parameters and topological parameters on system stability is analyzed. Results indicate that: two stable domains are emerged under load disturbance, the overall stability of asymmetric hydro turbine governing system is determined by the intersection area of the two stable domains. In addition, the system parameters and topological parameters both have obvious effect on system stability, which can be significantly improved by reasonable tuning of system parameters and optimization of water diversion system layout. [ABSTRACT FROM AUTHOR]

The paper presents a new composite structure made up of a double-layer microchannel structure, an impinging jet structure, and a turbulent flow structure. In this paper, the combination of these three structures improves the overall thermal performance of the model compared to the basic impingement-jet double-layer nested microchannel heat sinks (IDN-MHS) model. At Reynolds numbers ranging from 138.2 to 580.4 (0.25≤u in ≤1.05), the thermal performance of the model within introduction of bifurcations is enhanced compared to traditional models that only contain double-layer microchannel structures and impact jet structures. Using 3D printers and conducting experiments, it was discovered that numerical simulation and experimental images were generally consistent. Additionally, IDN-MHS with streaming vertical bifurcations, n=6 (IDN-MHS-VB6) performed well in numerical simulations, with a temperature decrease of 1.24K over IDN-MHS when compared to IDN-MHS. In addition, this model performs better than IDN-MHS with streaming vertical bifurcations, n=2, IDN-MHS with streaming vertical bifurcations, n=4, and IDN-MHS with streaming vertical bifurcations, n=8 (IDN-MHS-VB2/4/8). Compared to IDN-MHS, IDN-MHS-VB6 has the outstanding advantage of reducing substrate temperature while maintaining a relatively low pressure drop. • This structure is an innovative combination of double layer microchannel structure and bifurcation structure of impact jet structure. • In the designed composite structure, the highest substrate temperature is 1.23 K lower than IDN-MHS. • The innovative structure designed has an acceptable pressure drop. • The designed bifurcation structure can effectively increase the coolant flow rate and reduce the substrate temperature. • The IDN-MHS-VB6 allows the coolant to come into contact with more high-temperature areas, achieving cooling effect. [ABSTRACT FROM AUTHOR]

• Dynamic competition game models with low-carbon preferences are established. • The phenomenon of bifurcation and chaos in the dynamic game system are explored. • The impact of parameters on global stability is analyzed. • The profits of static and dynamic games are compared separately. Motivated by the low-carbon economic development, we study the competition issues in apparel supply chains considering consumers' low-carbon preferences. In this paper, we construct static and dynamic decision-making models under different game scenarios based on the centralized and decentralized frameworks. Firstly, we explore the critical conversion conditions between the centralized and decentralized frameworks with the static game models. The centralized model benefits the whole supply chain when the low-carbon investment coefficient is moderate. On the contrary, the decentralized model benefits the supply chain when the low-carbon investment coefficient is smaller or larger. Secondly, combined with the local and global bifurcation theory, we examine the complex effect of adjustment parameters on the dynamic system. The dynamic game systems show bifurcation, chaos, and multi-stability as the adjustment parameters change continuously. Therefore, we apply a hybrid chaos control method to stabilize the dynamic system. Thirdly, we compare the average profits in the dynamic game scenarios and show the complex relationships with the varying parameters. Finally, some management insights and suggestions are presented based on our findings. [ABSTRACT FROM AUTHOR]

• In this paper, through the following highlights, a hierarchical control structure microgrid based on a small-signal model and Hopf bifurcation theory are used. • Combining linear damping analysis method and nonlinear Hopf bifurcation analysis method, a stability analysis method based on oscillating trajectory is proposed. • Considering the oscillation phenomenon caused by changes the system model and control structure, and study the influence of microgrid secondary control on system stability under different oscillating trajectories and abrupt loads. • Using Hopf bifurcation theory and oscillation trajectory to delineate the parameter trajectories stable region, and analyze the changes of track stability region before and after hierarchical control. To the oscillation and stability problem caused by multi-scale and broadband electromagnetic dynamics among many isomerized power electronic devices in a microgrid, a small-signal model of hierarchical control structure microgrid and stability analysis method based on oscillation trajectories are proposed. Moreover, a hierarchical control structure is used as the research object in microgrid, and the analysis is performed based on the small-signal model and Hopf bifurcation theory. First, the small-signal model of the hierarchical control structure microgrid is established, combining the dominant eigenvalue and participation factor analysis methods, to analyze the influence of the controller and related sensitive parameters on the dynamic performance of the system. Then, based on the small-signal model and Hopf bifurcation theory, a stability analysis method based on oscillation trajectories is proposed. The relationship between different oscillation modes and limit cycles in the microgrid system and the influence of the sag control parameter values on the oscillation trajectory and stability domain of the system are researched on. Combining Hopf bifurcation theory and oscillation trajectory to delineate the stable domain of parameter trajectories, the influence of secondary control on the system stability is analyzed under different oscillation trajectories and load disturbances, revealing the corresponding relationship between the state trajectories of different oscillation modes and system stability of a hierarchical control structure microgrid. Based on the proposed oscillating trajectories, the stability analysis method has sufficient universality for studying the impact of system stability, establishing the parameter selection standards for the design of microgrids. Finally, according to the verification results, the correctness and applicability of above methods are verified. [ABSTRACT FROM AUTHOR]

In this paper, we study an intra- and interspecific competition system with the different diffusion rates in an unstirred chemostat. Due to the present of the different diffusion rates, the conservation principle for a classical standard chemostat model does not hold here. Firstly, we prove the existence, the uniqueness and asymptotic behaviors of positive solution of the single population system by using the degree theory. Secondly, by the degree theory and standard bifurcation theory, the existence and global structure of the coexistence solutions are investigated. The results show that when the maximum growth rates of two microorganisms with different diffusion abilities are not small, two competing microorganisms will coexist. Finally, numerical simulations are performed to illustrate that the interspecific interference can help the weaker competitor to win in the competition. [ABSTRACT FROM AUTHOR]

This paper investigates the critical condition whereby the compressed edge of a beam subjected to large bending exhibits a sudden lateral heeling. This instability phenomenon occurs through a mechanism different from that usually studied in linear theory and known as flexural–torsional buckling. An experimental test device was specifically designed and built to perform pure bending tests on soft materials. Thus, the experimental campaign provides not only the moment-curvature behavior of beams of narrow rectangular cross section, but also information regarding the post-critical lateral buckling behavior. To study the local bifurcation phenomenon, an analytical model is proposed in which a field of small transversal displacements, typical of the linear stability of thin plates, is superimposed on the large vertical displacement field of an inflexed beam in the nonlinear elasticity theory. Furthermore, numerous numerical simulations through nonlinear FE analysis have been performed. Finally, the results provided by the different methods applied were compared and discussed. • We study the lateral buckling of prismatic plate-like solids under finite bending. • The onset of buckling is quantified through the energy criterion. • A small out-of-plane perturbation is superposed to in-plane nonlinear displacement. • Upper bound of the critical curvature is compared with FE analyses and experiments. [ABSTRACT FROM AUTHOR]

For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this transition can be achieved in fundamentally different ways. This paper reviews 20 such 'Hopf-like' bifurcations for two-dimensional ODE systems with state-dependent switching rules. The bifurcations include boundary equilibrium bifurcations, the collision or change of stability of equilibria or folds on switching manifolds, and limit cycle creation via hysteresis or time delay. In each case a stationary solution changes stability and possibly form, and emits one limit cycle. Each bifurcation is analysed quantitatively in a general setting: we identify quantities that govern the onset, criticality, and genericity of the bifurcation, and determine scaling laws for the period and amplitude of the resulting limit cycle. Complete derivations based on asymptotic expansions of Poincaré maps are provided. Many of these are new, done previously only for piecewise-linear systems. The bifurcations are collated and compared so that dynamical observations can be matched to geometric mechanisms responsible for the creation of a limit cycle. The results are illustrated with impact oscillators, relay control, automated balancing control, predator–prey systems, ocean circulation, and the McKean and Wilson–Cowan neuron models. [ABSTRACT FROM AUTHOR]

Abstract This paper is regarded as a continuation of the paper "Principles for the application of bifurcation theory for the systematic analysis of nuclear reactor stability, Part1" with the intention to provide examples demonstrating the application of the bifurcation analysis method in the framework of reactor stability analysis. Hence, we continue with chapter 5 which is devoted to three examples: (1) two-phase flow stability analysis, (2) occurrence of a generalized Hopf bifurcation (GHB) during a real nuclear reactor stability test and (3) existence of a complex stability behaviour in an environment of a double Hopf bifurcation point (Hopf-Hopf bifurcation, HHB). The efficiency of the RAM-ROM method is demonstrated for an operating point of NPP Leibstadt for which a sufficient experimental and system code database is available. These three examples of system dynamics demonstrate the partly very complex stability behaviour of nonlinear systems which cannot be explained by the application of linear stability analysis methods such as the estimation of the decay ratio (as a linear stability indicator). The consequences of the found bifurcation types in examples 2 and 3 on the particular solution structure of the underlying dynamic system will be discussed by using their respective normal forms in order to provide the reader a more clear access to the complex system behaviour around these bifurcation points. In case of the Hopf-Hopf bifurcation, we only present a selected part of solutions in this paper and refer the reader to a future paper, where more details of this bifurcation type are summarized and consequences to the full system are interpreted. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider reaction–diffusion model with modified Leslie–Gower and Holling-type II functional response and by varying simultaneously three model parameters, our model exhibits different types of complex dynamics. This allowed us to delimit several bifurcation surfaces with higher codimension corresponding to: Turing, Turing-Transcritical, Turing–Bogdanov–Taken, Turing–Hopf–Andronov, Turing-Saddle–node. Moreover by varying at least three bifurcation parameters, we show that small variations in the ratio of the diffusion coefficients can significantly alter bifurcation structure. Finally, the paper ends with the emergence of spatio-temporal patterns via numerical simulations. These simultaneous parameter variations leaded to spatio-temporal local and global bifurcations which are always catastrophic. Our results give new insights about how simultaneous changes in environmental and life history parameters drive different distribution dynamics of predator–prey populations. This only underscores the importance of including global bifurcations in the analysis of food chain models. Such results can be used to improve ecological decision-making on species conservation. Highlights • We found five types of bifurcations in our model. • We have characterized the parameters that can lead to these bifurcations. • We characterized the complex domains of parameter space delimiting the different types of dynamics. • We have determined by simulation the types of dynamics corresponding to these instabilities. [ABSTRACT FROM AUTHOR]

Abstract In this paper the dynamics of differential equation with two linearly state-dependent delays is considered, with particular attention focused on non-resonant double Hopf bifurcation. Firstly, we identify the sufficient and necessary conditions of the double Hopf bifurcation by formal linearization, linear stability analysis and Hopf bifurcation theorem. Secondly, in the first time the method of multiple scales (MMS) is employed to classify the dynamics in the neighborhoods of two kinds of non-resonant double Hopf bifurcation points, i.e. Cases III and Ib, in the bifurcation parameters plane. Finally, numerical simulation is executed qualitatively to verify the previously analytical results and demonstrate the rich phenomena, including the stable equilibrium, stable periodic solutions, bistability and stable quasi-periodic solution and so on. It also implies that MMS is simple, effective and correct in higher co-dimensional bifurcation analysis of the state-dependent DDEs. Besides, the other complicated dynamics, such as the switch between torus and phase-locked solution, period-doubling and the route of the break of torus to chaos are also found in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the spatiotemporal dynamics and pattern formation of a space–time discrete intraguild predation model with self-diffusion are investigated. The model is obtained by applying a coupled map lattice (CML) method. First, using linear stability analysis, the existence and stability conditions for fixed points are determined. Second, using the center manifold theorem and the bifurcation theory, the occurrence of flip, Neimark-Sacker, and Turing bifurcations are discussed. It is shown that the patterns obtained are results of Turing, flip, and Neimark-Sacker instabilities. Numerical simulations are performed to verify the theoretical analysis and to reveal complex and rich dynamics of the model, such as times series, maximal Lyapunov exponent, bifurcation diagrams, and phase portraits. Interesting patterns like spiral pattern, polygonal pattern, and the combinations of patterns of spiral waves and stripes are formed. The CML model's results help to understand how a spatially extended, discrete intraguild predation model forms complex patterns. Notably, the continuous reaction–diffusion counterpart of the model under study is incapable of experiencing Turing instability. • Dynamics of a space–time discrete intraguild predation model with self-diffusion are investigated. • Interesting patterns like spiral pattern, polygonal pattern, and the combinations of patterns of spiral waves and stripes are formed. • The continuous reaction–diffusion counterpart of the model under study is incapable of experiencing Turing instability. [ABSTRACT FROM AUTHOR]

Highlights • The basic kinematic equation is established based on FEA. • The actuation compatibility of rigid-body motion is proposed. • The RRT method is adopted for the path planning of loaded pin-jointed bar mechanisms. • Actuation compatibility, shortest path and structural stability are mainly concerned. • An adaptive strategy is suggested to improve the sampling efficiency of RRT. Abstract Path planning of loaded pin-jointed bar mechanisms, typical of Pantadome, is discussed in this paper. In engineering, the path from the initial configuration to the target configuration generally cannot be determined easily because of the complicated constraint conditions. The basic kinematic equation of loaded pin-jointed bar mechanisms is hereby established based on FEA, and the driving condition of internal rigid-body (mechanism) displacements is presented for the length actuation of active members. A numerical strategy is proposed to trace the shortest path of pure mechanism displacement from the initial configuration to the given target configuration. With the emphasis on the constraints of structural stability and range of motion, the Rapidly-exploring Random Tree (RRT) method is adopted for the path planning of the loaded pin-jointed bar mechanisms. The RRT method is further modified to be applicable for the path planning when the target configuration is implicitly defined by its distance to be as close as possible to a geometrical boundary, at which the conventional RRT algorithm fails to track multiple feasible paths. An adaptive strategy is also suggested to improve the sampling efficiency of RRT. Considering loose and tight constraints of structural stability respectively, a loaded planar Pantadome is employed as the numerical example to investigate the validity of the path planning method proposed in this paper. [ABSTRACT FROM AUTHOR]

In the engineering practice, arches, such as arch bridges, are often subjected to localized loading. It is known that the nonlinear in-plane instability of shallow arches is caused by the significant in-plane bending action. The different localized loading produces very different in-plane bending distributions and so the instability of arches under localized loading would be quite different from that under a central point load or under a radial load uniformly distributed over the entire arch. However, there are no studies about the nonlinear instability and post-instability of arches under localized loading reported in the literature. This paper presents nonlinear in-plane analyses for fixed shallow circular arches under a localized uniform radial load. Novel theoretical solutions for nonlinear equilibrium, limit point instability, and bifurcation instability for arches under a localized uniform load are obtained, and new theoretical solutions of the certain modified slenderness switching the instability patterns of an arch under localized uniform loading are also obtained. It is found that the length of localized loading segment significantly influences the in-plane instability and post-instability responses of an arch. The limit point and bifurcation instability loads decrease with a decrease of the length of the localized loading segment. However, the modified slenderness switching instability patterns is found to increase with a decrease of the length of the localized loading segment. Comparisons against the finite element results show the theoretical solutions derived in this paper are accurate. These theoretical solutions provide comprehensive solutions for nonlinear instability and post-instability of fixed arches and they can reduce to those under a central point load or to extend to those under a uniform load over the entire arch. [ABSTRACT FROM AUTHOR]

This paper is focused on the pseudo bifurcations and the variety of periodic ratio in the periodic orbits near the primary of binary irregular asteroid system (22) Kalliope, which would help on trajectory design for asteroid missions and give a practical insight into the generation and dynamic behaviour of binary asteroid systems. In this paper, we find three basic pseudo bifurcations in the periodic orbit families near (22) Kalliope during the numerical continuation with the variation of Jacobian constant. We also discover a nonuple mixed bifurcations which possess the highest multiplicity of bifurcations ever found and consist of three pseudo tangent bifurcations, two period-doubling bifurcations, one pseudo period-doubling bifurcation, one Neimark-Sacker bifurcation, one pseudo Neimark-Sacker bifurcation, and one real saddle bifurcation. Moreover, we find that the periodic ratio in the periodic orbit family may change during the continuation. Based on plenty of numerical evidences, we summarize three astonishing and exciting conclusions about the relationship of the periodic ratio and (pseudo) bifurcations in the periodic motion near (22) Kalliope. Firstly, the pseudo period-doubling bifurcation shows up when the periodic ratio comes near a half-integer (i.e. 1.5:1, 2.5:1, 3.5:1). Furthermore, almost all the cuspidal changes of the periodic ratio are accompanied with tangent bifurcation or pseudo tangent bifurcation. In addition, an integer can be admitted as the asymptotic value of the periodic ratio at the end of continuation, if the Jacobian constant isn't stuck into its local extremum, yet a half-integer can not. [ABSTRACT FROM AUTHOR]

In the previous papers ( Kobayashi, 2017a, b ), the crack opening criterion was deduced from the proposed micro-crack evolution equation. To solve the discrepancies between the estimated and experimental strengths of ductile materials by considering the plastic/damage energy dissipation according to ASTM standard E1820-01, an improved version of the proposed crack opening criterion was proposed and successively applied to the ductile materials such as A533B steel, Al2024-T4 and SiAlon. With regard to the fracture progress, it is well known that the chaotic behavior of crack propagation seems to be caused by the bifurcation of the fracture mode. In this paper, the simulation of ductile fracture progress in notched FCC single crystal specimens characterized by different crystal orientations under the uniaxial tension is performed using the crystal plasticity finite element model (CPFE) to consider specifically the dependence of ductile fracture progress on the crystal orientation. The model was also integrated with a proposed micro-/macro-crack nucleation criteria deduced by two different stationary discontinuity bands characterized by the vanishing velocity condition. The simulated results were compared with the experimental ones. Both bifurcation mechanisms of the fracture mode of the simulated and experimental results were then studied using the proposed crack opening criterion based on the bifurcation structure characterized by two different stationary discontinuity bands. It can be concluded that the proposed crack opening criterion and its improved application including the proposed diagram contribute to study fracture physical mechanisms. [ABSTRACT FROM AUTHOR]

This paper takes the four types of resource allocation (randomly oriented, relationship-oriented, cooperation oriented, and knowledge-embedded) as its premise and investigates the complex characteristics of knowledge flow network evolution in strategic alliances, taking into account the mutual variance effects of the evolution mechanism. Existing research has neglected the differences in resource allocation types, by and large employed statistical analysis methods, and identified only the linear relationships among experimental variances of cross-sectional data. The present study differs from existing research in the following ways: First, we thoroughly consider the multi-faceted nature of resource allocation. Second, we use the method of multi-agent imitation according to perspective of dynamic system evolution and the principle of phase theory, allowing the explicitly analysis of nonlinear functional logic, forms and patterns in the variance. Finally, we analyze the appropriateness of different resource allocation models. Our paper features several significant findings: (1) The evolution of the knowledge flow network of a strategic alliance can produce a bifurcation phenomenon composed of saddle-node bifurcation and transcritical bifurcation. (2) The number of nodes exhibits a logarithmic growth distribution, the connection intensity and the network gain exhibit exponential growth distributions, and the connectivity and knowledge flow frequency are mutually influential in the form of a power function. (3) Knowledge-embedded resource allocation is most effective for improving the knowledge flow rate of networks and can further supply ample impetus for evolution. (4) Cooperation-oriented resource allocation is most beneficial for quickly propelling the network into the evolution realm. (5) Relationship-oriented resource allocation can aid the network in capturing more profit. Furthermore, this research is beneficial for understanding the key problems of each resource allocation model and the evolution of strategic alliance in knowledge flow networks. Our proposed methods and framework can be more widely applied to the fields of complex networks, knowledge management, and strategic innovation. [ABSTRACT FROM AUTHOR]

In orbital maneuvering, the mass variation due to fuel consumption has an obvious impact on the dynamics of tethered system, which cannot be neglected. The contributions of the work are mainly shown in two aspects: 1) the improvement of the model; 2) the analysis of dynamics characteristics. As the mass is variable, and the derivative of the mass is directly considered in the traditional Lagrange equation, the expression of generalized force is complicated. To solve this problem, the coagulated derivative is adopted in the paper; besides, the attitude dynamics equations derived in this paper take into account the effect of mass variation and the drift of orbital trajectory at the same time. The bifurcation phenomenon, the pendular motion angular frequency, and amplitudes of tether vibration revealed in this paper can provide a reference for the parameters and controller design in practical engineering. In the article, a dumbbell model is adopted to analyze the dynamics of tethered system, in which the mass variation of base satellite is fully considered. Considering the practical application, the case of orbital transfer under a transversal thrust is mainly studied. Besides, compared with the analytical solutions of librational angles, the effects of mass variation on stability and librational characteristic are studied. Finally, in order to make an analysis of the effect on vibrational characteristic, a lumped model is introduced, which reveals a strong coupling of librational and vibrational characteristics. [ABSTRACT FROM AUTHOR]

This paper evaluates several state-feedback control design methods for a multi-phase interleaved DC–DC boost converter with an arbitrary number of legs. The advantages of state-feedback control laws are numerous since they do not burden the system with the introduction of further zeros or poles that may lead to poorer performance as far as overshoot and disturbance rejection is concerned. Both static and dynamic full state-feedback control laws are designed based on the converter’s averaged model. Building on previous work, this paper introduces significant extensions on the investigation of several undesirable bifurcation phenomena. In the case of static state-feedback it is shown that interleaving can give rise to more severe bifurcation phenomena, as the number of phases is increased, leading to multiple equilibria. As a remedy, a bifurcation analysis procedure is proposed that can predict the generation of multiple equilibria. The novelty of this paper is that this analysis can be integrated into the control design so that multiple equilibria can be completely avoided or ruled out of the operating region of interest. The proposed control laws are digitally implemented and validated in a 2-leg case study using both simulation and experimentation. [ABSTRACT FROM AUTHOR]

In the commented paper, the authors consider a three-dimensional system and analyze the presence of Shilnikov chaos as well as a Hopf bifurcation. On the one hand, they state that the existence of a chaotic attractor is verified via the homoclinic Shilnikov theorem. The homoclinic orbit of this system is determined by using the undetermined coefficient method, introduced by Zhou et al. in [Chen's attractor exists, Int. J. Bifurcation Chaos 14 (2004) 3167–3178], a paper that presents very serious shortcomings. However, it has been cited dozens of times and its erroneous method has been copied in lots of papers, including the commented paper where an even expression for the first component of the homoclinic connection is used. It is evident that this even expression cannot represent the first component of a Shilnikov homoclinic connection, an orbit which is necessarily non-symmetric. Consequently, the results stated in Section 3, the core of the paper, are worthless. On the other hand, the study of the Hopf bifurcation presented in Section 4 is also wrong because the first Lyapunov coefficient provided by the authors is incorrect. [ABSTRACT FROM AUTHOR]

The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the stationary problem for a Lotka–Volterra competition system with advection under homogeneous Dirichlet boundary conditions. By using global bifurcation theory, we establish the sufficient conditions on terms of the birth rates of two competing species assuring the existence of positive solutions. Moreover, some sufficient conditions for the nonexistence of positive solutions are also given. These contrast with the mathematical analyses carried out by Kuto and Tsujikawa (2015) and Wang and Yan (2015), where the corresponding Neumann problem is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear dynamic characteristics and bifurcation of Al-doped graphene are studied. The nonlinear dynamic model of Al-doped graphene impacted by hydrogen atoms is developed where the nonlocal effect of a graphene is considered. The natural frequency of the system is obtained, the system's drift coefficient and diffusion coefficient are verified, and the stationary probability density function of the system's dynamic response is given. The condition of stochastic bifurcation is determined, and the fractal boundary of the safe basin is provided. Finally, the reliability function of the system is solved, and the probability density of the first-passage time is determined. Theoretical analysis and numerical simulation show that stochastic bifurcation occurs in the variation of parameters; the area of safe basin decreases when the intensity of the atom's impact increases. The results of this paper are helpful for the application of Al-doped graphene in hydrogen storage. [ABSTRACT FROM AUTHOR]

This paper present and discusses proposals for the codification of efficient design approaches for cold-formed steel columns affected by local-distortional (L-D) interaction. These proposals, based on the Direct Strength Method (DSM), were developed, calibrated and validated on the basis of experimental and numerical (shell finite element) failure load data concerning columns with several cross-section shapes (plain, web-stiffened and web-flange-stiffened lipped channels, hat-sections, zed-sections and rack-sections) and obtained from investigations carried out by various researchers. Three types of L-D interaction are taken into account, namely “true L-D interaction”, “secondary-local bifurcation L-D interaction” and “secondary-distortional bifurcation L-D interaction”. Moreover, previously available DSM-based design approaches developed to handle column L-D interactive failures are reviewed and their merits are assessed and compared with those exhibited by the present proposals. The paper also presents reliability assessments of the failure load predictions provided by the available and proposed DSM-based design approaches, following the procedure prescribed by the current version of the North American Specification for the Design of Cold-Formed Steel Structural Members. [ABSTRACT FROM AUTHOR]

The smooth and discontinuous oscillator with fractional derivative damping under combined harmonic and random excitations is investigated in this paper. The short memory principle is introduced so that the evolution process of the oscillator with fractional derivative damping can be described by the Markov chain. Then the stochastic generalized cell mapping method is used to obtain the steady-state probability density functions of the response. The stochastic response and bifurcation of the oscillator with fractional derivative damping are discussed in detail. We found that both the smoothness parameter, the noise intensity, the amplitude and frequency of the harmonic force can induce the occurrence of stochastic P-bifurcation in the system. Monte Carlo simulation verifies the effectiveness of the method we adopt in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we ascertain the global λ -structure of the set of positive and negative solutions bifurcating from u = 0 for the semilinear elliptic BVP − d Δ u = λ 〈 a , ∇ u 〉 + u + λ u 2 − u q in Ω , u = 0 on ∂ Ω , according to the values of d > 0 and the integer number q ≥ 4. Figs. 1.1–1.3 summarize the main findings of this paper according to the values of d and q. Note that the role played by the parameter λ in this model is very special, because, besides measuring the strength of the convection, it quantifies the amplitude of the nonlinear term λ u 2 . We regard to this problem as a mathematical toy to generate solution loops and isolas in Reaction Diffusion equations. [ABSTRACT FROM AUTHOR]

In this paper we present a bifurcation analysis of two periodically forced Duffing oscillators coupled via soft impact. The controlling parameters are the distance between the oscillators and the difference in the phase of the harmonic excitation. In our previous paper http://arXiv:1602.04214 (P. Brzeski et al. Controlling multistability in coupled systems with soft impacts [11] ) we show that in the multistable system we are able to change the number of stable attractors and reduce the number of co-existing solutions via transient impacts. Now we perform a detailed path-following analysis to show the sequence of bifurcations which cause the destabilization of solutions when we decrease the distance between the oscillating systems. Our analysis shows that all solutions lose stability via grazing-induced bifurcations (period doubling, fold or torus bifurcations). The obtained results provide a deeper understanding of the mechanism of reduction of the multistability and confirmed that by adjusting the coupling parameters we are able to control the system dynamics. [ABSTRACT FROM AUTHOR]

We investigate the hydrodynamic limit of a vapor–noncondensable gas mixture in a pressure gradient between two walls. Earlier papers based on conventional asymptotic analysis techniques predict the emergence of a boundary layer of noncondensables which completely blocks the vapor flow (Takata and Aoki, 2001; Aoki et al., 2003). This “ghost effect” (Sone, 2007) contradicts physical intuition. In the present paper we reveal the bifurcation structure of the underlying transport operator and combine it with an appropriate macroscopic scaling. As a result, the hydrodynamic limit describes the coexistence of a streaming mode of vapor with the other component at rest thus avoiding the ghost effect. For sake of clarity, the paper restricts to a simplified setting (discrete velocity model, mechanically identical particles). However, the results also apply in more general situations. [ABSTRACT FROM AUTHOR]

This paper is concerned with multiple solutions of a singular nonlinear boundary value problem (BVP) on the interval [ 0 , 1 ] , which arises in a study of the laminar flow in a porous pipe with an expanding or contracting wall. For the singular nonlinear BVP, the correct boundary conditions are derived to guarantee that its linearization has a unique smooth solution. Then a numerical technique is proposed to find all possible multiple solutions. For the suction driven pipe flow with the expanding wall (e.g. α = 2 ), we find a new solution numerically and classify it as a type VI solution. The computed results agree well with what can be obtained by the bifurcation package AUTO. In addition, we also construct asymptotic solutions for a few cases of parameters, which agree well with numerical solutions. These serve as validations of our numerical results. Thus we believe that the numerical technique designed in the paper is reliable, and may be further applied to solve a variety of nonlinear equations that arise from other flow problems. [ABSTRACT FROM AUTHOR]

The singularity theory is applied to study the bifurcation behaviors of a reduced rotor model obtained by nonlinear transient POD method in this paper. A six degrees of freedom (DOFs) rotor model with cubically nonlinear stiffness supporting at both ends is established by the Newton's second law. The nonlinear transient POD method is used to reduce a six-DOFs model to a one-DOF one. The reduced model reserves the dynamical characteristics and occupies most POM energy of the original one. The singularity of the reduced system is analyzed, which replaces the original system. The bifurcation equation of the reduced model indicates that it is a high co-dimension bifurcation problem with co-dimension 6, and the universal unfolding (UN) is provided. The transient sets of six unfolding parameters, the bifurcation diagrams between the bifurcation parameter and the state variable are plotted. The results obtained in this paper present a new kind of method to study the UN theory of multi-DOFs rotor system. [ABSTRACT FROM AUTHOR]

In this paper, we propose an impulsive predator–prey model with communicable disease in the prey species only and investigate its interesting biological dynamics. By the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we have deduced the sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the proposed model. We also give the existences of the “infection-free” periodic solution and the “predator-free” solution. Finally, numerical results validate the effectiveness of theoretical analysis for the proposed model in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the lateral–torsional buckling of elastoplastic steel beams under pure bending considering various cross-section geometries. Critical buckling moment expressions for elastic beams are well documented. In contrast, less attention has been devoted to the lateral–torsional buckling phenomenon in elastoplastic regime. When considering short beams (with sufficiently low slenderness), plastic zones will develop before buckling occurs. The problem being faced here is however much more complex than the classical problem of an elastoplastic beam subjected to an axial compressive force. Under such loading, plasticity occurs instantaneously and evolves uniformly over the cross-section and along the beam length whereas, in the other case, plasticity will spread gradually and the plastic zones will change with the loading. The main objective of the present paper is to develop original analytical solutions for the elastoplastic lateral–torsional buckling of perfectly straight beams. A general formulation based on a previously developed 3D plastic bifurcation theory is first proposed and then applied to the cases of two specific cross-section geometries, namely rectangular and I profiles. For the sake of simplicity, transverse shear strains are neglected in the analysis. The von Mises yield criterion with a linear isotropic hardening is adopted. In the case of a rectangular cross-section, closed-form solutions are obtained for the elastoplastic critical buckling moment, which is shown to depend on the geometric and material parameters of the beam, including the yield stress. For validation purposes, all the analytical solutions are compared against the results of numerical computations performed with an in-house program based on a shell finite element formulation. Analytical and numerical results are in very good accordance, making the analytical method presented here an efficient and precise tool to analyze the elastoplastic lateral–torsional buckling phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order (and an integer-order) memristor-based system with the flux-controlled memristor characterized by smooth quadratic nonlinearity is proposed and detailed dynamical analysis is carried out by means of theoretical and numerical methods. To be more specific, stability of each equilibrium point in the equilibrium set is analyzed for the integer-order memristive system. Meanwhile, dynamical behavior depending on the initial states of the memristor is investigated and dynamical bifurcation depending on the slope of the memductance function is also considered. The bifurcation analysis is verified by numerical methods, including phase portraits, bifurcation diagrams, Lyapunov exponents spectrum, and Poincaré mappings. For the fractional-order case, based on the fractional-order stability theory, stability analysis is carried out just for a certain equilibrium point. Moreover, bifurcation behavior depending on the incommensurate order is discussed by virtue of numerical methods based on the Adams–Bashforth–Moulton algorithm. This paper indicates how the fractional order model and the initial state of the memristor extend the dynamical behaviors of the traditional chaotic systems. [ABSTRACT FROM AUTHOR]