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Aiming at the wedge friction damper for freight train bogie, considering Dankowicz dynamic friction, the mechanical model of a three-degree-of-freedom inclined impact vibration system with gap and dynamic friction, is simplified. The mechanical model of the system is established, the motion equation of the system is obtained, and the motion state and conditions of the system are analyzed. The Poincare map is constructed by selecting a fixed collision section, and the response of the system is solved by the fourth-order Runge-Kutta numerical method with variable step size. The transition process of the system motion and the phenomenon of sticking and chatter are analyzed by numerical simulation when the external excitation frequency changes. The results show that: 1) Under certain parameters, with the change of excitation frequency, the system undergoes periodic doubling bifurcation, inverse periodic doubling bifurcation, Grazing bifurcation and Hopf bifurcation, and there is a "periodic bubble" phenomenon in the system motion. When the system excitation frequency is between 3.35–3.55, 4.425–6.12, and 7.34–7.758, the system motion has chatter and sticking phenomena; when the system excitation frequency is between 1.75–3.24 and 3.92–4.425, the sticking phenomenon disappears, and only the chatter phenomenon exists. 2) When other parameters remain unchanged, and the mass ratio decreases from 1.15 to 0.85, nonlinear dynamic phenomena such as the transition between periodic bubbles and chaotic bubbles will be found. In this paper, the bifurcation and chaos characteristics of the impact vibration system of the wedge friction damper are studied, and the rich friction-induced vibration forms such as chatter and sticking are revealed, which provides a reference for improving the stability of vehicle operation and the selection of parameters in vehicle vibration reduction design in engineering practice. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of nonlinear vibration phenomena in the arm system of an industrial robot. The presented mathematical model of the robot takes into account the flexibility of the joints, which results in low-frequency vibrations in the arm. The study of vibration phenomena has been carried out using analytical, numerical and experimental methods. Special attention has been paid to bifurcation phenomena. The influence of two bifurcation parameters on the behaviour of the robot arm was studied. It was shown that the amplitude and frequency of the harmonic excitation create a nonlinear effect on the vibration amplitudes of the links. In bifurcation regions, the vibration amplitudes can even differ several times depending on the direction of changes in the bifurcation parameter. In general, the results indicate that, contrary to common practice, it is worth paying attention to nonlinear phenomena when analysing robot vibrations. [ABSTRACT FROM AUTHOR]

The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of a discrete-time Cournot game with time delay, where the interactions of one public firm and n private firms on the market are considered. The production of the public firm is adjusted based on the past production levels of the private firms. At the same time, the productions of the private firms are updated with respect to the past production of the public firm. Two equilibrium points are determined for the discrete-time nonlinear mathematical model. The analysis of the stability reveals that the boundary equilibrium point is a saddle point, while the positive one, under some conditions, is asymptotically stable for any time delays. Numerical simulations illustrate the complex dynamic behaviour of the system. [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 show the positive solutions set for one-dimensional p -Laplacian problem with sign-changing weight contains a reversed S -shaped continuum. By figuring the shape of unbounded continuum of positive solutions, we identify the interval of bifurcation parameter in which the p -Laplacian problem has one or two or three positive solutions according to the asymptotic behavior of nonlinear term at 0 and ∞. The proof of the main result is based upon bifurcation technique. [ABSTRACT FROM AUTHOR]

Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility of equilibria and their stability properties are discussed. A pertinent quantity ( ℛ 0 ), known as the reproduction number, is calculated and it is shown that the formulated system undergoes transcritical, saddle-node, Hopf and Bogdanov–Takens bifurcations on the variation of ℛ 0 . The analytically obtained results are validated through numerical simulations. The results obtained from this study indicate that a substantial rate of job generation by self-employed individuals has a stabilizing effect on the system. Moreover, self-employment along with informal skill acquisition through engaging in informal work proves to be an effective measure in curbing the issue of unemployment in society. [ABSTRACT FROM AUTHOR]

In this paper is considered a microalgae growth model under the influence of sunlight. The model is a two-dimensional system of the first order Ordinary Differential Equations (ODE) with a ten-dimensional parameter space. For this model, we study the existence of equilibrium points and their stability, and determine a bifurcation of the system when the value of some parameters is varied. The Lambert ω function is used to calculate equilibrium points and apply the linearization technique to provide their stabilities. By varying the value of some parameters numerically, we found a transcritical bifurcation of the system and show stability regions of the equilibrium points in parameter diagrams. The bifurcation shows that the microalgae have a minimum sustainable nutrition supply and have a minimum light intensity that plays an important role for survival in a chemostat which has a certain depth. The results can be used to design a chemostat in optimizing the growth of microalgae. [ABSTRACT FROM AUTHOR]

This paper investigates a simple memristor emulator consisting of a diode bridge and a capacitor. It exhibits pinched hysteresis loops, and what is more striking is the higher frequency, as it operates up to greater than 5 MHz. Based on the proposed memristor, a higher-frequency Colpitts circuit was established. According to the mathematical model of the system, the system only possesses one unstable equilibrium point. Period doubling bifurcation, reverse periodic doubling bifurcation, different types of periodic and chaotic orbits, transient chaos, coexisting bifurcations and offset boosting are depicted. More interestingly, it has coexisting multiple attractors with different topologies, such as a chaotic attractor accompanied with periodic orbits, period-1 orbits with bicuspid structure and periodic-2 orbits with tridentate structure. Moreover, a hardware circuit using discrete components was fabricated and experimental measurements were consistent with the MATLAB numerical results, further confirming the real feasibility of the proposed circuit. [ABSTRACT FROM AUTHOR]

A new smooth model is proposed in this paper to eliminate the non-differentiability of several types of limits in power flow models. The proposed smooth model accurately represents power system static models with limits as a continuously differentiable function. Analytic results are developed to show that each solution of the proposed smooth model is arbitrarily close to a solution of the corresponding original power flow model with limits. The proposed smooth model includes a wide range of devices with physical limits, such as generators, transformers, HVDCs, phase shifters, and shunts. In addition, it is shown that every generic static bifurcation in the original model is transformed into a saddle-node bifurcation in the smoothed model. Hence, the search for bifurcations in voltage stability assessment can be greatly simplified. Several numerical studies of the proposed smooth model on a 9241-bus power system and on a 13659-bus power system have shown promising results. [ABSTRACT FROM AUTHOR]

For the Gerdjikov-Ivanov equation, by using the method of dynamical system, this paper investigates the exact explicit solutions with the form ... In the given parameter regions, more than 14 explicit exact parametric representations are presented. [ABSTRACT FROM AUTHOR]

With widespread application of voltage source converter (VSC) as a key energy-conversion power electronic device by using the phase-locked loop (PLL) technique for synchronization, the system dynamics has become much complicated. In this paper, the nonlinear dynamics and transient stability of the PLL-based VSC system are investigated, within a unified framework of the (normalized) generalized swing equation. It is found that there are three different types of bifurcation, including the generalized saddle-node, Hopf, and homoclinic bifurcations. Within the coexistence parameter region, the basin boundary of the stable equilibrium point shows either a closed-loop or a fish-like pattern. With the help of the equal area criterion (EAC), the transient stabilities under different transient disturbances including short circuit, voltage dip, and power rise are analyzed. Because the equivalent damping of the VSC is state-dependent, the theoretical results based on the EAC are examined. Furthermore, based on the analytical results from the generalized swing equation, the principle for all major transient stability enhancement methods is uncovered. All these findings are well verified by extensive electromagnetic transient simulations. Therefore, the generalized swing equation provides a deeper physical insight and plays a crucial role in transient stability problems in power-electronic-dominated power systems, similar to the swing equation in traditional power systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new four-dimensional hyperchaotic system derived from the chaotic maps of Peter de Jong's simple attractor and the discrete iterative function. In this work, our main motivation is to explore a link that can be developed to generate hyperchaos from 2D chaotic system. An association between 2D system and a higher order one was not studied in the previous literature. In fact, in the literature, there is no two-dimensional systems from which we are able to associate a four-dimensional one. In this context, a special interest is reserved to Peter de Jong system due to its exceptional advantages such as hypersensitivity and velocity. The challenge in this paper is the development of a four-dimensional hyperchaotic system associated to the Peter de Jong one while conserving its important characteristics such as hypersensitivity, velocity and the lack of equilibrium. The system structure that we will detail is different from other hyperchaotic systems widely suggested in the literature. In fact, the proposed attractor does not display any equilibrium point. A mathematical study is carried out in order to obtain time plots, Lyapunov exponents spectrum and bifurcation diagram. Finally, we will prove the high sensitivity of this system relative to its initial condition by simulations and experimental observations. [ABSTRACT FROM AUTHOR]

In this paper, by using dynamical system theorems we study the bifurcation of a second-order ordinary differential equation which can be obtained from many nonlinear partial differential equations via traveling wave transformation and integrations. We present all the bounded exact solutions of this second-order ordinary differential equation which contains four parameters by normalization and classification. As a result, one can obtain all possible bounded exact traveling wave solutions including soliatry waves, kink and periodic wave solutions of many nonlinear wave equations by the formulas presented in this paper. As an example, all bounded traveling wave solutions of the modified regularized long wave equation are obtained to illustrate our approach. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to research dynamic properties of a mechanical system consisting of a ball jumping between a movable baseplate and a fixed upper stop. The model is constructed with one degree of freedom in the mechanical oscillating part. The ball movement is generated by the gravity force and non-harmonic oscillation of the baseplate in the vertical direction. The impact forces acting between the ball and plate and the stop are described by the nonlinear Hertz contact law. The ball motion is then governed by a set of two nonlinear ordinary differential equations. To perform their solving, the Runge-Kutta method of the fourth order with adaptable time step was applied. As the main result, it is shown that the systems exhibit regular, irregular, and chaotic pattern for different choices of parameters using the newly introduced 0-1 test for chaos, detecting bifurcation diagram, and researching Fourier spectra. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper discusses the bifurcation and stability behavior of (automotive) turbochargers with full-floating ring bearings. Turbocharger rotors exhibit a highly nonlinear behavior due to the nonlinearities introduced by the floating ring bearings. A flexible multibody model of the rotor/bearing system is presented. Numerical run-up simulations are compared with corresponding test rig measurements. The nonlinear oscillation effects are thoroughly investigated by means of simulated and measured rotor vibrations. The influence of various system parameters on the bifurcation behavior of the rotor/bearing system is analyzed. The article examines rotors supported in full-floating ring bearings with plain circular bearing geometry in the inner and outer oil gap. By recapitulating the well-known oil whirl and oil whip phenomena for single and double oil film bearings, the paper gives an overview on the fundamental dynamic effects occurring in turbocharger systems. [ABSTRACT FROM AUTHOR]

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings. [ABSTRACT FROM AUTHOR]

This paper investigates mathematical models of predator-prey systems where a transmissible disease spreads only among the prey species. Two mathematical models are proposed, analysed and compared to assess the influence of hidden or explicit resources for the predator. The predator is assumed to be a generalist in the first model and a specialist on two prey species in the second one. Existence and boundedness of the solutions of the models are established, as well as local and global stability and bifurcations. The equilibria of two systems possessing the same biological meaning are compared. The study shows that the relevant ecosystem behaviour including stability switching, extinction and persistence for any species depends on four important parameters, viz., the reproduction rate and the infection rate of the main prey, the mortality rate of infected prey and the reproduction rate of the alternative prey. This study ultimately indicates that the simpler formulation with the hidden resource already captures the salient features of the ecosystem. Therefore, modeling explicitly the substitute prey is not needed unless a particular emphasis is placed on the alternative resource behaviour. In such case, the extended model is preferable, at the expenses of a more complicated formulation and analysis. Ultimately, the choice of the model to be used should be guided by the reasons of its formulation and the answers that are sought. [ABSTRACT FROM AUTHOR]

In this paper, a deterministic model for transmission of an epidemic has been proposed by dividing the total population into three subclasses, namely susceptible, infectious and recovered. The incidence rate of infection is taken as a nonlinear functional along with time delay, and treatment rate of infected is considered as Holling type III functional. We have structured a deterministic transmission model of the epidemic taking into account the factors that affect the epidemic transmission such as social and natural factors, inhibitory effects and numerous control measures. The delayed model has been analyzed mathematically for two equilibria, namely disease-free equilibrium (DFE) and endemic equilibrium. It is found that DFE is locally and globally asymptotically stable when the basic reproduction number (R 0) is less than unity. It has also been shown that the delayed system for DFE at R 0 = 1 is linearly neutrally stable. The existence of an endemic equilibrium has been shown and found that under some conditions, endemic equilibrium is locally asymptotically stable, and is globally asymptotically stable when R 0 > 1 . Further, the endemic equilibrium exhibits Hopf bifurcation under some conditions. Finally, an undelayed system has been analyzed, and it is shown that at R 0 = 1 , DFE exhibits a forward bifurcation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. By constructing a Poincar'e map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system. [ABSTRACT FROM AUTHOR]

Earthquake is a natural phenomenon that occurs due to the movement of plate tectonics that released energy during slip along a fault in the earth. This phenomenon has been extensively studied by a spring-block model. The aim of this paper is to analyze dynamical behavior of a single degree of freedom spring-block model which represents a stick-slip fault under the effect of non-viscous damping forces. In particular, we analyze the stability of equilibrium points and bifurcation of the model, and illustrate by numerical analysis. [ABSTRACT FROM AUTHOR]

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured). [ABSTRACT FROM AUTHOR]

In this paper, we investigate pattern formation in Keller-Segel chemotaxis models over a multidimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as chemoattraction rate increases. Then using Crandall-Rabinowitz local theory with being the bifurcation parameter, we obtain the existence of nonhomogeneous steady states of the system which bifurcate from this homogeneous steady state. Stability of the bifurcating solutions is also established through rigorous and detailed calculations. Our results provide a selection mechanism of stable wavemode which states that the only stable bifurcation branch must have a wavemode number that minimizes the bifurcation value. Finally, we perform extensive numerical simulations on the formation of stable steady states with striking structures such as boundary spikes, interior spikes, stripes, etc. These nontrivial patterns can model cellular aggregation that develop through chemotactic movements in biological systems. [ABSTRACT FROM AUTHOR]

The use of plastic is very widespread in the world and the spread of plastic waste has also reached the oceans. Observing marine debris is a serious threat to the management system of this pollution. Because it takes years to recycle the current wastes, while their amount increases every day. The importance of mathematical models for plastic waste management is that it provides a framework for understanding the dynamics of this waste in the ocean and helps to identify effective strategies for its management. A mathematical model consisting of three compartments plastic waste, marine debris, and recycle is studied in the form of a system of ordinary differential equations. After describing the formulation of the model, some properties of the model are given. Then the equilibria of the model and the basic reproduction number are obtained by the next generation matrix method. In addition, the global stability of the model are proved at the equilibria. The bifurcations of the model and sensitivity analysis are also used for better understanding of the dynamics of the model. Finally, the numerical simulations of discussed models are given and the model is examined in several aspects. It is proven that the solutions of the system are positive if initial values are positive. It is shown that there are two equilibria E 0 and E ∗ and if B R < 1 , it is proven that E 0 is globally stable, while when B R > 1 , the equilibrium E ∗ exists and it is globally stable. Also, at B R = 1 the model exhibits a forward bifurcation. The sensitivity analysis of B R concludes that the rates of waste to marine, new waste, and the recycle rate have most effect on the amount of marine debris. [ABSTRACT FROM AUTHOR]

This paper deals with a predator-prey model with Beddington-DeAngelis functional response, in which a protection zone is created for the prey species. Whether the combination of the protection zone and the Beddington-DeAngelis functional response can yield new results or not is of interest. The result reveals that they jointly produce a new critical value, which is smaller than that determined by either the protection zone or the functional response singly. As a result, rather different stationary patterns can be found and the combined effects are very prominent. Then the effect of the parameter k in the Beddington-DeAngelis functional response is studied. The result deduces that as k is large enough, there exists a unique positive stationary solution and it is linearly stable except a special case. Actually, we can obtain that the positive stationary solution is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

The paper investigates the complex nonlinear behavior of a fractional order four dimension power system (FOFDPS). The discrete mathematical model of the FOFDPS is derived and presented. The equilibrium points along with the Eigen values of commensurate and incommensurate FOFDPS are presented. The existence of chaotic oscillations are supported by a positive Lyapunov exponent. Bifurcation plots are derived for both parameters and fractional orders to show the impact of the same on the dynamic behavior of FOFDPS. Having shown the existence of such complex behaviors in the FOFDPS, we present an adaptive fractional order sliding mode control (FOASMC) to suppress the chaotic oscillations. Numerical results are presented to support the theoretical results. [ABSTRACT FROM AUTHOR]

The degenerate Bogdanov-Takens system x˙ = y-(a1x+a2x3); y˙ = a3x + a4x3 has two normal forms, one of which is investigated in [Disc. Cont. Dyn. Syst. B (22)2017, 1273-1293] and global behavior is analyzed for general parameters. To continue this work, in this paper we study the other normal form and perform all global phase portraits on the Poincarée disc. Since the parameters are not restricted to be sufficiently small, some classic bifurcation methods for small parameters, such as the Melnikov method, are no longer valid. We find necessary and sufficient conditions for existences of limit cycles and homoclinic loops respectively by constructing a distance function among orbits on the vertical isocline curve and further give the number of limit cycles for parameters in different regions. Finally we not only give the global bifurcation diagram, where global existences and monotonicities of the homoclinic bifurcation curve and the double limit cycle bifurcation curve are proved, but also classify all global phase portraits. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae (immature) stage. Both the Mosquito and human populations are divided into susceptible and infective class. Susceptible class of mosquito population is further divided into mature and immature. The model is analyzed by using stability theory of nonlinear ordinary differential equations. Basic reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal activity. In addition, it is observed that biting rate of mosquito, transmission efficiency of parasitic infection from infective human to mosquito and critical value of maturation delay are the key parameters determining the stability switch in the system. Numerical simulation is also carried out to confirm the analytical results obtained in the paper. [ABSTRACT FROM AUTHOR]

Many experimental studies have demonstrated that ducted premixed flames exhibit stable limit cycles in some regions of parameter space. Recent experiments have also shown that these (period-1) limit cycles subsequently bifurcate to period-${2}^{n}$, quasiperiodic, multiperiodic or chaotic behaviour. These secondary bifurcations cannot be found computationally using most existing frequency domain methods, because these methods assume that the velocity and pressure signals are harmonic. In an earlier study we have shown that matrix-free continuation methods can efficiently calculate the limit cycles of large thermoacoustic systems. This paper demonstrates that these continuation methods can also efficiently calculate the bifurcations from the limit cycles. Furthermore, once these bifurcations are found, it is then possible to isolate the coupled flame–acoustic motion that causes the qualitative change in behaviour. This information is vital for techniques that use selective damping to move bifurcations to more favourable locations in the parameter space. The matrix-free methods are demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic $G$-equation solver. The methods find limit cycles and period-2 limit cycles, and fold, period-doubling and Neimark–Sacker bifurcations as a function of the location of the flame in the duct, and the aspect ratio of the steady flame. [ABSTRACT FROM PUBLISHER]

Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effects of small-amplitude, additive, white Gaussian noise on stable sliding motion. For equations that are static in directions parallel to the switching manifold, the distance of orbits from the switching manifold approaches a quasi-steady-state density. From this density we calculate the mean and variance for the near sliding solution. Numerical results of a relay control system reveal that the noise may significantly affect the period and amplitude of periodic solutions with sliding segments. [ABSTRACT FROM AUTHOR]

• A model for the population dynamics of age-structured criminal gangs with correctional intervention measures is proposed. • The existence of backward bifurcation is determined by the adolescent population. • We fitted the gang model against the crime data and provide forecast for the cumulative number of reported cases. • Global sensitivity analysis is carried out to determine the parameters that strongly drive the dynamics of the model. • The existence of periodic trajectories (Hopf bifurcation) for the criminal gang model is studied. The prevalence of criminal gang activities in the society has continued to be a huge burden to mankind. Despite several attempts by the government and non-governmental organizations in curtailing the activities of criminal gangs, new criminal gangs are beginning to emerge with associated criminal cases on the high side, thereby causing social unrest. This paper examines the impact of correctional intervention measures on the population dynamics of the criminal gangs in Nigeria, following an age-structured paradigm. The existence of backward bifurcation is presented sequel to the coexistence of gang free equilibrium and gang endemic equilibrium when the reproduction number is less than unity. Also, the model exhibits periodic trajectories (Hopf bifurcation) as a result of coexistence among the criminal gang classes. Using the Nigeria crime data (from 1993 to 2013) as obtained from Elsevier Data in Brief, we analyze the criminal gang model quantitatively and provide the sociological implications of the results. The numerical results obtained from this work show that if at least 60 % of adolescents between 8–17 years who commit crimes are apprehended with prompt prosecution and correction, we can potentially eradicate adolescent delinquencies from the population and thus control the entire criminal gangs' population. [ABSTRACT FROM AUTHOR]

This paper focuses on the application of different tyre models to analyse the shimmy phenomenon. Tyre models with the Magic Formula and a non-constant relaxation length are introduced. The energy flow method is applied to compare these tyre models. A trailing wheel suspension is used to analyse shimmy stability and to evaluate the differences between tyre models. Linearisation and nonlinear techniques, including bifurcation analysis, are applied to analyse this system. Extending the suspension model with lateral flexibility and structural damping reveals more information on shimmy stability. Although the nonlinear tyre models do not change the stability of equilibria, they determine the magnitude of the oscillation. It is concluded that the non-constant relaxation length should be included in the shimmy analysis for more accurate results at large amplitude. [ABSTRACT FROM AUTHOR]

The focus of this paper is to investigate the dynamics of seizure activities by using the Epileptor coupled model. Based on the coexistence of seizure-like event (SLE), refractory status epilepticus (RSE), depolarization block (DB), and normal state, we first study the dynamical behaviors of two coupled oscillators in different activity states with Epileptor model by linking them with slow permittivity coupling. Our research has found that when one oscillator in normal states is coupled with any oscillator in SLE, RSE or DB states, these two oscillators can both evolve into SLE states under appropriate coupling strength. And then these two SLE oscillators can perform epileptiform synchronization or epileptiform anti-synchronization. Meanwhile, SLE can be depressed when considering the fast electrical or chemical coupling in Epileptor model. Additionally, a two-dimensional reduced model is also given to show the effect of coupling number on seizures. Those results can help to understand the dynamical mechanism of the initiation, maintenance, propagation and termination of seizures in focal epilepsy. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlocal dispersal problem with a nonlocal term arising in population dynamics: where is a bounded domain, , represents the nonlocal dispersal operator with continuous and non-negative dispersal kernel. The kernel is assumed to be non-negative and is allowed to have a degeneracy in a smooth subdomain of . When is either positive or vanishes in a subdomain, we respectively investigate the existence, multiplicity and asymptotical stability of positive steady states under the local/global variation of parameter by means of sub-supersolution method, Lyapunov-Schmidt reduction, and bifurcation theory. [ABSTRACT FROM AUTHOR]

Biodegradation, the disintegration of organic matter by microorganism, is essential for the cycling of environmental organic matter. Understanding and predicting the dynamics of this biodegradation have increasingly gained attention from the industries and government regulators. Since changes in environmental organic matter are strenuous to measure, mathematical models are essential in understanding and predicting the dynamics of organic matters. Empirical evidence suggests that grazers' preying activity on microorganism helps to facilitate biodegradation. In this paper, we formulate and investigate a stoichiometry-based organic matter decomposition model in a chemostat culture that incorporates the dynamics of grazers. We determine the criteria for the uniform persistence and extinction of the species and chemicals. Our results show that (1) if at the unique internal steady state, the per capita growth rate of bacteria is greater than the sum of the bacteria's death and dilution rates, then the bacteria will persist uniformly; (2) if in addition to this, (a) the grazers' per capita growth rate is greater than the sum of the dilution rate and grazers' death rate, and (b) the death rate of bacteria is less than some threshold, then the grazers will persist uniformly. These conditions can be achieved simultaneously if there are sufficient resources in the feed bottle. As opposed to the microcosm decomposition models' results, in a chemostat culture, chemicals always persist. Besides the transcritical bifurcation observed in microcosm models, our chemostat model exhibits Hopf bifurcation and Rosenzweig's paradox of enrichment phenomenon. Our sensitivity analysis suggests that the most effective way to facilitate degradation is to decrease the dilution rate. [ABSTRACT FROM AUTHOR]

A mathematical model has been created and investigated that simulates the relationship between predator and prey with the appearance of an infectious disease in the predator population and additional food reservoirs for the predator. The prey declines its rate of growth due to it is enforced by the predator's rage to seek out a place where it will feel scared and safe. The bounds, existence, and uniqueness of the solution of the suggested model are examined. The local stability of the model at feasible equilibrium points was calculated. The Lyapunov function is utilized to identify the basin of attraction for each equilibrium point. The possibility of bifurcation when the parameters vary is also carefully discussed. Numerical simulations were then used to validate the analytical conclusions and provide insight into how parameter changes impacted the model's dynamics. Different attractors of the system are obtained, such as point, periodic, and nonlinear centers. [ABSTRACT FROM AUTHOR]

In this paper the mathematical modeling of an 8/6 switched reluctance machine (SRM) is carried out and the performance in motoring mode operation is studied in Matlab/Simulink environment. SRM is a highly nonlinear machine due to variable inductance and frequent switching of phase current so to study the non linear dynamic behaviors in SRM is important to improve the performance. For the variable speed conditions the reference speed is tuned for attaining the required speed. Due to that in 8/6 SRM hardware circuit is designed at close loop condition, with various reference speeds and the corresponding performance is investigated. [ABSTRACT FROM AUTHOR]

This paper research deals with the accuracy and bifurcation problem of grey Verhulst model with thought of taking reciprocal. Firstly, we get a new form of solution by taking reciprocal to grey Verhulst model and verify a considerable improvement of its accuracy has been improved greatly with examples. Then, we further discuss the chaos and period-doubling bifurcation phenomena of grey Verhulst model, and conclude that the period-doubling bifurcation will delay or early occur, or even disappear, relative to traditional logistic map with different parameter values. Numerical simulation examples are given to support the theoretical analysis of period-doubling bifurcation. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on modeling and oscillatory stability analysis of a wind turbine with doubly fed induction generator (DFIG). A detailed mathematical model of DFIG wind turbine with vector-control loops is developed, based on which the loci of the system Jacobian's eigenvalues have been analyzed, showing that, without appropriate controller tuning a Hopf bifurcation can occur in such a system due to various factors, such as wind speed. Subsequently, eigenvalue sensitivity with respect to machine and control parameters is performed to assess their impacts on system stability. Moreover, the Hopf bifurcation boundaries of the key parameters are also given. They can be used to guide the tuning of those DFIG parameters to ensure stable operation in practice. The computer simulations are conducted to validate the developed model and to verify the theoretical analysis. [ABSTRACT FROM PUBLISHER]

In this paper we investigate the dynamics and bifurcations of an oil-well drill-string model that takes the form of a neutral delay differential equation. We consider the torsional mode of the drill-string and investigate the associated stick--slip motion. To analyze the model we develop numerical continuation routines based on Fourier methods since existing routines based on polynomial approximations are unable to cope with the presence of arbitrarily weakly damped modes. We find "resonance peaks" in the dynamics where a high-frequency mode is superimposed on the underlying periodic behavior, causing large torsional waves in the drill-string. We show that the resonance peaks are robust to small perturbations in the friction parameters but disappear if static friction forces are neglected completely. [ABSTRACT FROM AUTHOR]

In this paper the global patterns that result from local interactions between players on a two-dimensional lattice are studied. The assumptions on interaction between players are based on the Prisoner's Dilemma game that has been used extensively in game theory and in the study of biological systems. Each player is located on a square lattice, and is assumed to cooperate or defect, based on mimicking the neighbor with the highest cumulative score from the preceding round of play. The edges of the lattice are glued to form a torus. Computer simulations are conducted for different sized lattices, different payoff values, and different initial conditions. Though the paper is primarily concerned with player behavior without self-interaction, some results with self-interaction are also included. The influence of "ideal" cooperators on the evolution of the system dynamics is also studied. Three generic regimes of behavior are identified. Complex global patterns with complicated dynamics and sometimes unpredictable results occur. Steady-state solutions, simple and complex periodic solutions, and traveling waves are observed depending on the initial conditions and the payoff values. [ABSTRACT FROM AUTHOR]

The aim of the paper is to investigate the bifurcation behavior of the power-factor-correction (PFC) boost converter under a conventional peak current-mode control. The converter is operated in continuous-conduction mode. The bifurcation analysis performed by computer simulations reveals interesting effects of variation of some chosen parameters on the stability of the converter. The results are illustrated by time-domain waveforms, discrete-time maps and parameter plots. An analytical investigation confirms the results obtained by computer simulations. Such an analysis allows convenient prediction of stability boundaries and facilitates the selection of parameter values to guarantee stable operation. [ABSTRACT FROM AUTHOR]

One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1. In this paper we consider an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. We extend the fundamental bifurcation theorem to this evolutionary model. We apply the results to an evolutionary version of a Ricker model with an added Allee component. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena, such as backward bifurcation induced strong Allee effects. [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]

The upstream offshore multi-phase well-pipeline-riser installations are facing huge challenges related to slugging flow: An unstable flow regime where the flow rates, pressures and temperatures oscillate in the multi-phase pipelines. One typical severe slug is induced by vertical wells or risers causing the pressure to build up and hence originates the oscillating pressure and flow. There exist many negative consequences related to the severe slugging flow and thus lots of investments and effort have been put into reducing or completely eliminating the severe slug. This paper reviews in details the state-of-the-art related to analysis, detection, dynamical modeling and elimination of the slug within the offshore oil & gas Exploration and Production (E&P) processes. Modeling of slugging flow has been used to investigate the slug characteristics and for design of anti-slug control as well, however most models require specific facility and operating data which, unfortunately, often is not available from most offshore installations. Anti-slug control have been investigated for several decades in oil & gas industry, but many of these existing methods suffer the consequent risk of simultaneously reducing the oil & gas production. This paper concludes that slug is a well defined phenomenon, but even though it has been investigated for several decades the current anti-slug control methods still have problems related to robustness. It is predicted that slug-induced challenges will be even more severe as a consequence of the longer vertical risers caused by deep-water E&P in the future. [ABSTRACT FROM AUTHOR]

We discuss a computational model that describes stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals. Let Toff and Ton be the time that the stimulus is off and on, respectively. The behavior was studied by direct numerical simulation in a grid of (Toff, Ton) values in a 2007 paper of Noest, van Ee, Nijs, and van Wezel. They found that both alternating and repetitive sequences of percepts can appear stably, sometimes even for the same values of Toff and Ton. Longer Toff, however, always leads to a situation where, after transients, only repetitive sequences of percepts exist. We incorporate Toff and Ton explicitly as bifurcation parameters of an extended mathematical model of the perceptual choices. We elucidate the bifurcations of periodic orbits responsible for switching between alternating and repetitive sequences. We show that the stability borders of the alternating and repeating sequences in the (Toff, Ton) -parameter plane consist of curves of limit point and period-doubling bifurcations of periodic orbits. The stability regions overlap, resulting in a wedge with bistability of both sequences. We conclude by comparing our modeling results with the experimental results obtained by Noest, van Ee, Nijs, and van Wezel. [ABSTRACT FROM AUTHOR]