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Nonlinear mixed models are essential for data analysis due to their versatility and adaptability to many research objectives and data formats. Testing misspecification is crucial to selecting a working nonlinear model. A useful and simpler model is often chosen using variance component tests. Nonlinear models are rarely studied in the literature, unlike linear models, which have numerous successful test development attempts. The latter test requires linearity between the answer and the explanatory factors. Thus, we use an existing linearization technique to build a linear model using pseudo-responses. If random effects were needed in the original nonlinear mixed model, the pseudo-responses vector inherits a mixed linear model representation. Simulation experiments and an application to a real-world bioassay data set evaluate this permutation test. [ABSTRACT FROM AUTHOR]

Nonlinear normal modes (NNMs) are defined as curved invariant structures (manifolds) in the phase-space of a nonlinear dynamical system, which confine the trajectories initiated on them to themselves and hence provide a reduced order subspace for the system to evolve. In this work, NNMs, obtained through graph style parameterization method, are used to study synchronization dynamics of two non-isochronous, frequency detuned limit cycle oscillators (LCOs) under displacement-based/reactive and velocity-based/dissipative coupling, also considering the effect of delayed interactions. The NNMs contain closed curves corresponding to either the in-phase or out-of-phase synchronized oscillations. The motion initiated on these NNMs is found to evolve strictly on them, unless it encounters a fixed point or closed orbit with an out-of-plane unstable direction, in which case it may even transition to the other manifold. In all other cases, the motion settles onto a stable fixed point or orbit on either manifold if existent, or on to a quasi-periodic orbit lying between the two manifolds in the absence of one. The NNMs are used to uncouple the governing equations of the system, directly giving the in-phase and out-of-phase synchronization frequencies and stability. Parametric study using averaged equations as well as the direct numerical integration-based evolution of the original system on the NNMs is used to identify various bifurcations. The properties of NNMs are tested for qualitatively different motions hence determined. NNMs for the delay coupled oscillators are obtained, by first expanding the delay terms in a Taylor series. It is found that even a small delay ( < 1 % of LCOs time period) brings a significant change in the behavior of the system. The quantitative predictions made by NNM in this case are found to be good for finite delay times ( ≈ 10 % of LCOs time period), while qualitative agreement was achieved for even larger delays. The results obtained here agree with prior work in the literature, at the same time extending them to hitherto unexplored parameter range and provide a new perspective on the same from the point of view of NNMs. [ABSTRACT FROM AUTHOR]

Dynamic pricing depends on the understanding of uncertain demand. We ask the question whether a stochastic system is sufficient to model this uncertainty. We propose a novel paradigm based on statistical analysis of recurrence quantification measures. The paradigm fits nonlinear dynamics by simultaneously optimizing both the determinism and the trapping time in recurrence plots and identifies an optimal time delay embedding. We firstly apply the paradigm on well-known deterministic and stochastic systems including Duffing systems and multi-fractional Gaussian noise. We then apply the paradigm to optimize the sampling of empirical point process data from RideAustin, a company providing ride share service in the city of Austin, Texas, the USA, thus reconstructing a period-7 attractor. Results show that in deterministic systems, an optimal embedding exists under which recurrence plots exhibit robust diagonal or vertical lines. However, in stochastic systems, an optimal embedding often does not exist, evidenced by the inability to shrink the standard deviation of either the determinism or the trapping time. By means of surrogate testing, we also show that a Poisson process or a stochastic system with periodic trend is insufficient to model uncertainty contained in empirical data. By contrast, the period-7 attractor dominates and well models nonlinear dynamics of empirical data via irregularly switching of the slow and the fast dynamics. Findings highlight the importance of fitting and recreating nonlinear dynamics of data in modeling practical problems. [ABSTRACT FROM AUTHOR]

Under the background of ‘mass entrepreneurship and innovation’, Chinese colleges and universities have strengthened students’ entrepreneurial and innovative abilities. The article first analyses the reasons why applied universities should strengthen innovation and entrepreneurship education. On this basis, the evaluation index system of students’ innovation and entrepreneurship ability is constructed. The thesis uses the nonlinear structural model to complete the index weight setting. Finally, the paper verifies the effectiveness of the combined evaluation model through the data on innovation and entrepreneurship of college students in an university where applied. At the same time, the article proposes measures for optimising the ecological environment of innovation and entrepreneurship education for colleges and universities.

We consider the N-vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion with prescribed symmetries. Our construction relies on the discrete reduction of the system by twisted subgroups of the full symmetry group that rotates and permutes the vortices. Our approach formalises and extends ideas outlined previously by Tokieda (C R Acad Sci, Paris I 333:943–946, 2001) and Soulière and Tokieda (J Fluid Mech 460:83–92, 2002) and allows us to prove the existence of several 1-parameter families of periodic orbits. These families either emanate from equilibria or converge to collisions possessing a specific symmetry. Our results are applied to show existence of families of small nonlinear oscillations emanating from the Platonic solid equilibria. [ABSTRACT FROM AUTHOR]

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states. [ABSTRACT FROM AUTHOR]

We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1 : 2 resonance. Under detuning, this "Fermi resonance" typically leads to normal modes losing their stability through period-doubling bifurcations. For cubic potentials, this concerns the short axial orbits, and in galactic dynamics, the resulting stable periodic orbits are called "banana" orbits. Galactic potentials are symmetric with respect to the coordinate planes whence the potential—and the normal form—both have no cubic terms. This Z 2 × Z 2 symmetry turns the 1 : 2 resonance into a higher-order resonance, and one therefore also speaks of the 2 : 4 resonance. In this paper, we study the 2 : 4 resonance in its own right, not restricted to natural Hamiltonian systems where H = T + V would consist of kinetic and (positional) potential energy. The short axial orbit then turns out to be dynamically stable everywhere except at a simultaneous bifurcation of banana and "anti-banana" orbits, while it is now the long axial orbit that loses and regains stability through two successive period-doubling bifurcations. [ABSTRACT FROM AUTHOR]

Business cycles denote oscillations in economy as a result of downturns and expansions. The macroeconomic variable under our investigation is income as derived by the dynamic interaction with capital, consumption and investment. In this paper, a Kaldorian business cycle model is used to simulate real dynamics so that nonlinear techniques such as recurrence quantification analysis, Poincaré Plot and related quantifiers can be applied. Analysis of chaos brings evidences on fractal dimension and entropy measures for both real data and model's simulations. The final goal is to discover whether real and simulated business cycle dynamics have similar characteristics and validate the model as a suitable tool to simulate reality. [ABSTRACT FROM AUTHOR]

In this paper, we study a fast explicit operator splitting method for space fractional nonlinear Schrödinger equation in one (1D), two (2D) and three dimensions (3D) with periodic boundary conditions. The equation is split into linear and nonlinear parts: the linear part is solved by the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size; the nonlinear subequation is then solved analytically due to the availability of a closed-form solution. The rigorous analysis of the discrete mass conservation principle and the convergence rate of the proposed algorithm are proved. The theoretical results show the proposed method is L 2 unconditionally stable, second order accurate in time, whereas the spatial accuracy depends on the regularity of the solution. Numerical experiments for 1D, 2D and 3D cases demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Dry drilling only with the assistance of an auger is a reliable and realistic approach to remove abundant soils from the side of a bit in the harsh, dry conditions on the Moon. Based on an elementary analysis, using Janssen's model to reflect the coupling effect among the different components of the stress, the present paper models the conveying dynamics along the helical groove and the sampling mechanism in the centering hole of the stem for an auger drilling into lunar soil simulant. Combining the two parts as well as a simple cutting model for the bit, a whole drilling model is established to investigate the complicated relation among the conveying ability of the auger, the coring rate, and drilling parameters such as the penetration and rotation speeds. The relation is revealed by the complicated transition between different sub-models with the help of the physical transition conditions. A series of experiments with constant penetration and rotation speeds are conducted to verify the model. Three aspects of characteristics of the drilling dynamics are manifested, (i) the loads on the bit are almost independent of penetration; (ii) three obvious drilling stages with respect to cut per revolution are grouped; (iii) a linear relationship is found between the coring rate and the revolution per penetration. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively. The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem (LCP) algorithm and the trial-and-error algorithm. Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot. [ABSTRACT FROM AUTHOR]

We discuss a novel microscopic model for collective decision-making interacting multi-agent systems. In particular we are interested in modeling a well known phenomena in the experimental literature called equality bias, where agents tend to behave in the same way as if they were as good, or as bad, as their partner. We analyze the introduced problem and we prove the suboptimality of the collective decision-making in the presence of equality bias. Numerical experiments are addressed in the last section. [ABSTRACT FROM AUTHOR]

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem (NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a constraint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects. [ABSTRACT FROM AUTHOR]

We present analytical and numerical studies of nonstationary resonance processes in a system with four degrees of freedom. The system under consideration can be considered as one of the simplest geometrically nonlinear discrete models of an elastic beam supported by nonlinear elastic grounding support. Two symmetrically distributed discrete masses reflect the inertial properties of the beam, two angular springs simulate its bending stiffness. The longitudinal springs, as is usual in systems of oscillators, reflect the tensile stiffness and two transversal springs simulate the reaction of grounding support. Dealing with low-energy dynamics, we singled out the equations of transversal motion corresponding to the approximation of two coupled oscillators with nonlocal nonlinearity in elastic forces. We have analyzed this model using the concept of limiting phase trajectories (LPT). LPT's concept was recently developed to study the nonstationary resonance dynamics. An analytical description of intensive interparticle energy exchange was obtained in terms of nonsmooth functions, which is consistent with numerical results. We have identified two dynamic transitions the first of which corresponds to the instability of out-of-phase normal mode and the second one is a transition from the intense energy exchange to the energy localization on the initially excited oscillator. Special attention was paid to the influence of bending stiffness on the conditions that ensure the implementation of each of the dynamic transitions. [ABSTRACT FROM AUTHOR]