Abstract A planar system has been proposed in the paper Rankin et al. (Nonlinear Dyn 66:681–688, 2011) to understand the canard explosion detected in a 6D aircraft ground dynamics model. A specific feature of this minimal 2D system is a critical manifold with a single fold and an asymptote. In this paper, we provide a high-order analytical prediction (in fact, up to any wanted order) of the canard

Abstract This paper investigates the problem of designing a dissipative controller for interval type-2 nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition descriptions. To explore a generalized model for MJFSs under realistic situations, the coexistence of incompletely known transition rates and mismatched membership functions is considered in MJFS models, and the corresponding

Abstract This paper concerns an investigation into the control of the transient vibration of an Euler–Bernoulli beam using a symmetric single-sided vibro-impact nonlinear energy sink (SSSVI NES). The non-dimensional system of equations is derived by using the Galerkin method. Consideration and theoretical analysis of the impact dynamics of the device is carried out by introducing the impact modes.

Abstract The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors

Abstract This paper deals with chaos synchronization problem between two different uncertain fractional-order (FO) chaotic systems with disturbance based on FO Lyapunov stability analysis method. A T–S fuzzy neural network model as a universal approximator is constructed to approximate those uncertain terms and unknown parameters. An adaptive sliding mode control scheme is established, and the adaptive

Abstract This paper deals with localized waves in the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in the incompressible fluid. Based on Hirota’s bilinear method, N-soliton solutions related to Boiti–Leon–Manna–Pempinelli equation are constructed. Novel nonlinear wave phenomena are obtained by selecting appropriate parameters to N-soliton solutions, and time evolutions of different kinds

Abstract Both imaginary value off-axis solitons and imaginary value off-axis vortex solitons are analytically obtained in nonlocal nonlinear media. The imaginary value off-axis solitons can do the snakelike propagations resulting from that the soliton phase \(\Theta \) are period functions, and the propagation paths (including propagation directions and reverse points) of such solitons can be controlled

Abstract We discuss the role played by the time correlation properties of stochastic sources and by model nonlinearities in single-degree of freedom energy-harvesting systems. After transforming the state equations into energy-angle coordinates, we apply a stochastic projection operator technique to obtain the system power balance equation. The latter allows to evaluate both the magnitude of the power

Abstract This study presents an analytical solution for the nonlinear forced vibration response of bridged carbon nanotube (CNT)-based mass sensors subjected to different types of thermal loading and external harmonic excitations. The structure undergoes a temperature change through its thickness when considering three different distribution patterns of the temperature, namely uniform, linear, and

Abstract This paper proposes an adaptive neural impedance control (ANIC) strategy for electrically driven robotic systems, considering system uncertainties and external disturbances. For the considered robotic system, the joint velocities and armature currents are assumed to be unknown and unmeasured, and an adaptive observer is then designed to estimate its unknown states using a neural network. Based

Abstract In this article, we consider a predator–prey system with constant rate of harvesting, which exhibits Hopf and Bogdanov–Takens bifurcations under certain parametric conditions. The parametric space under which the system enters into Hopf bifurcation is investigated. By constructing suitable Lyapunov function, global stability results are obtained. Here, death rate and harvesting rate are taken

Abstract This paper deals with analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled nth-order ordinary differential equations in the presence of a nonvanishing at \(x=0\) or even unbounded on the time interval \([0,\infty )\) time-varying high-frequency oscillating perturbation w(t, x). The obtained results generalize

Abstract In this work, based on the nine kinds of rub-impact scenarios of one single translational joint, we discuss 42 kinds of coupling rub-impact scenarios of double translational joints with subsidence for a triplex member including crosshead slider, piston rod, and piston slider. The two sliders are connected by a flexible piston rod. The flexible piston rod alternates between a straight rod and

Abstract Based on Darboux transformation, we generate breather solutions sitting on zero background via module resonance for complex modified KdV equation. Then, some novel soliton molecules, breather molecules and breather-soliton molecules are obtained theoretically by module resonance and velocity resonance. Further, we study the higher-order breather-positons with zero background on the basis of

Abstract This work presents a novel method for the analytical and numerical solution of an n-term fractional nonlinear dynamical system. Two simple methods, commonly known to vibration engineers, namely the method of averaging and harmonic balance method, are utilized to obtain the analytical and numerical solution, respectively. The differential equation is derived from a physical problem. The primary

Abstract The wind-induced vibration of cables has been widely studied over the past decades because of cables’ many applications in cable-stayed, suspension, and tied-arched bridges, and power transmission lines. They have been mostly investigated through research conducted on rigid model cables with a finite length and circular cross-sectional geometry that represents a section model of a long cable

Abstract This paper mainly aims to explore the propagation behaviors of computer virus over complex networks under the combined effects of network topology and removable storage media. To this end, a dynamical model is established and analyzed theoretically, including the outbreak threshold, equilibria and their global dynamics. It is found from the systematic analysis that the virus will die out or

Abstract In the present work, we have studied a diffusive tritrophic food chain model in which the species at each trophic level interact in accordance with Crowley–Martin functional response under mixed boundary conditions. Using degree theory and fixed point index-based methods, we have proved the existence of the positive solutions of the proposed system. We have proved the permanence of the positive

Abstract We investigated an incompressible viscous liquid film flow over a rotating vertical cylinder of radius R and of infinite length rotating with a uniform angular velocity \(\varvec{\Omega }\) about its axis. The surface of the vertical cylinder is non-uniformly heated where the temperature varies linearly in the downstream direction. The flow is assumed to be axisymmetric, and the component

Abstract This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate drilling-induced vibrations, by considering idealized drag bits characterized either by multiple angular offsets between the blades or by a combination of full and partial blades, a departure from the symmetric bit of the RGD model

Abstract An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the \((2+1)\)-dimensional (D) sine-Gordon (SG) equation into the \((1+1)\)-D SG equation and obtain

Abstract Spike-frequency adaptation, which reduces the firing rate of a neuron during a constant stimulus, is a prominent property observed in many neurons. In this work, we studied the effects of the \(I_{\mathrm{AHP}}\) spiking adaptation on the information transmission and efficiency of the Morris–Lecar (ML) neuron model in the spike-timing coding scheme. We showed that this kind of adaptation caused

Abstract In this work, we present a comprehensive assessment of the Fisher information measure and statistical complexity measures based on Euclidean distance, Wootters distance and Jensen–Shannon divergence, regarding their abilities to (planar-) distinguish between/among (1) chaos and periodicity; (2) different degrees of periodicities; (3) different chaotic regimes; and (4) chaos and noise, and

Abstract The traditional nonlinear energy sink (NES), i.e., a smooth and cubic NES, can cause stable higher branch of response of primary systems with increasing excitation forcing. For this reason, the traditional NES is only effective in a certain excitation range. A kind of non-smooth NES with descending stiffness is proposed for expanding this effective range. The non-smooth NES has a higher cubic

Abstract This research proposes a parametric method to design dynamic compensator for high-order quasi-linear systems. According to the solutions of high-order generalized Sylvester equations, the completely parametric expressions of both the left and right eigenvector matrices and dynamic compensator are established. Based on the proposed method, we transform the closed-loop system into a linear time-invariant

Abstract Algal blooms are increasing in coastal waters worldwide. The study on the features of algal pollution in water bodies and the ways to eliminate them is of vital importance. Preventing, treating, and monitoring algal blooms can be an unanticipated cost for a water system. To tame algal bloom in a lake, the government provides funds through budget allocation. In this paper, we propose a mathematical

Abstract In this article, we present a system of coupled short pulse equations as integrability condition of associated generalized linear eigenvalue problem. We obtain system of \(\mathcal {PT}\)-symmetric short pulse equation (SPE) by using suitable reduction condition. In order to investigate the dynamics of loop solitons for nonlocal SPE, we use hodograph transformation to transform standard SPE

Abstract Bistability, the presence of alternative stable states, is an important feature of population models as it indicates that long-term predictions are dependent on the current population density. Two distinct kinds of bistability re-occur in population modelling studies, Allee Bistability and Positive Bistability. In this article, we show that a novel codimension-3 bifurcation, the cusp-transcritical

Abstract Quarter car models of vehicles rolling on wavy roads lead to limit cycles of travel speed and acceleration with period doublings and bifurcation effects for appropriate driving force parameters. In case of narrow-banded road excitations, speed jumps occur, additionally. This has the consequence that the driving speed becomes turbulent. Bifurcation and jump effects vanish with growing vehicle

Abstract In this paper, we investigate the asymptotic stability of the probability density function (pdf) of the states of a class of nonlinear SDEs. We use the Detailed-balance condition as the condition of stability for stochastic processes. Based on the definition of asymptotic stability of the pdf of the SDE, we introduce two notions of probability stability for trajectories of the SDE. The stabilizing

Abstract This paper is concerned with the global regulation via output feedback for the time-delay nonlinear systems with unknown continuous output function and unknown growth rate. Different from the existing literature, the output is perturbed by an unknown continuous function, and nonlinearities are upper bounded by unmeasured states multiplying an unknown constant and a polynomial of the output

Abstract A nonautonomous Gross–Pitaevskii equation with a partially nonlocal nonlinearity and a linear and parabolic potential is discussed, and a projecting expression between nonautonomous and autonomous equations is found. Via the projecting expression and utilizing the Darboux transformation method, diversified exact solutions, especially including a crossed Akhmediev and Ma breather solution,

Abstract This paper develops a design method for the interconnections of a network of Andronov–Hopf oscillators such that the system exhibits a desired strange attractor. Because of the structure of the oscillators, the desired behavior can be achieved via weak linear coupling, which destabilizes the oscillators’ phase difference. First, a set of sufficient conditions are established that result in

Abstract This study proposes a modified recurrence quantification analysis, called global recurrence quantification analysis (GRQA). It is well known that the recurrence threshold is an important parameter in traditional recurrence quantification analysis. However, in existing researches, the selection of recurrence thresholds is often based on ‘rules of thumb.’ As many studies have shown, recurrence

Abstract In this study, identification of nonlinear aerodynamic systems based on an improved nonlinear state-space modeling approach is presented to predict transonic aeroelastic behaviors of aircraft structures. It starts with identifying a linear state-space aerodynamic model by using the eigensystem realization algorithm and observer/Kalman filter identification methods. Subsequently, the remaining

Abstract We present a computational model which mainly concentrates on the effect of adjusting the signal strength of game from an agent to its a neighbor by considering the information quantity in individual’s database to study the evolutionary prisoner’s dilemma game on directed-weighted square lattices. In this model, each agent considers the current and historical payoff both obtained from the

Abstract In this study, mem-springs and mem-dashpots from a newly introduced family of mem-models are used as fundamental building blocks in hysteresis modeling. The usefulness of such assemblies of mem-models is investigated for both simulation and system identification. First, numerical simulations demonstrate the general capability of these models to describe strain ratcheting behaviors. Next, system

Abstract This paper addresses the guaranteed cost sampled-data controller synthesis and analysis problems with application to nonlinear chaotic systems. A linear parameter-varying (LPV) model is utilized to represent the nonlinear behaviour of the chaotic system while the gap between the measured and real parameters of the controller and plant are considered as bounded uncertainties. Using the LPV

Abstract In this paper, we design a memristive system involving magnetic coupling with time-delayed feedback. In a way of autaptic connection, the memristive magnetic coupling feedback is mapped into a neuronal model with ion-channel effect. Compared with the resistive coupling feedback in line with proposed autaptic connection, the memristive magnetic coupling feedback can enhance firing rates more

Abstract Identification of nonlinear systems, especially with multiple local nonlinearities exhibiting disproportional ratios of the degree of nonlinearity and present at a single or multiple spatial locations, is a highly challenging inverse problem. Identification of such complex nonlinear systems cannot be handled easily by the existing conventional restoring force or describing function methods

Abstract Linear time-delay feedback method makes the stable system generate the infinite-dimensional hyper-chaos, which possesses more than one positive Lyapunov exponent, infinite-dimensional, a wider chaotic parameter range, and multi-attractors, including the single-scroll attractor, the double-scroll attractor, and the composite multi-scroll attractor. The infinite-dimensional hyper-chaotic multi-attractors

Abstract A new nonlinear adaptive control strategy for electrohydraulic active suspensions with the hysteretic leaf spring is proposed to improve suspension performances of heavy vehicle. The nonlinear hysteresis property of leaf spring, described and experimentally validated with the Bouc–Wen model, is transformed into linear system by Takagi–Sugeno (T–S) fuzzy approach. Based on the derived T–S fuzzy

Abstract The paper presents a new concept of absorbing car body vibrations, which consists in a modification of the construction of the classical mono-tube hydraulic shock absorber by the introduction of an additional inner cylinder with an auxiliary piston. By making an appropriate selection of the system parameters, one may obtain the damping force characteristics dependent on the excitation amplitude

Abstract A complex modified short pulse (mSP) equation and a nonlocal mSP equation are presented. The integrability and the covariant property of both new equations are shown by constructing their corresponding Lax pair and Darboux transformation, respectively. For the complex mSP equation, some multiple smooth soliton, cuspon soliton, loop soliton, breather and rogue wave solutions are constructed

Abstract This paper mainly addresses the finite-time tracking problem of pure-feedback systems with indifferentiable non-affine functions. A novel adaptive fuzzy finite-time command filtered scheme is proposed by remodeling the non-affine functions. The control scheme consists of the fuzzy logic systems with modified minimal learning parameter technique, the command filtered scheme and the finite-time

Abstract This paper studies the transfer of energy accompanying the impact of two otherwise linear, viscously damped, single-degree-of-freedom oscillators, one of which is driven by harmonic base motion. A semi-analytical solution of the oscillator equations of motion, in which the times of impact are determined by bisection, is used to simulate the responses while the parameters of the system are

Abstract In this paper, we propose and numerically study a nonlinear, asymmetric, passive metamaterial that achieves giant non-reciprocity with (i) broadband frequency operation and (ii) robust signal integrity. Previous studies have shown that nonlinearity and geometric asymmetry are necessary to break reciprocity passively. Herein, we employ strongly nonlinear coupling, triangle-shaped asymmetric

The licence type in the original article was incorrect and should be CC BY and not CC BY NC.

Abstract We systematically develop a Riemann–Hilbert approach for the quartic nonlinear Schrödinger equation on the line with both zero boundary condition and nonzero boundary conditions at infinity. For zero boundary condition, the associated Riemann–Hilbert problem is related to two cases of scattering data: N simple poles and one Nth-order pole, which allows us to find the exact formulae of soliton

Abstract Nonlinear dynamic analysis of the assembled structures involves the complex nonlinearity of the joint interfaces. By combining the multi-harmonic balance method with the Newton–Raphson iteration process, a high-efficiency nonlinear dynamic analysis method is proposed to analyze the steady-state dynamic responses influenced by the hysteresis nonlinearity of the joint interfaces. The proposed

Abstract This study investigates the longitudinal flight control problem of air-breathing hypersonic vehicles subject to the asymmetric angle of attack (AoA) constraint. With the help of introduced tangent errors, the proposed control becomes low complexity in both structure and expression, especially for the non-adaptive control algorithm in the altitude loop. The asymmetric AoA constraint, which

Abstract 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

Abstract In this paper, the mechanism of switching combination synchronization the controlled Duffing oscillator with Van der Pol system and Pendulum system is studied. Based on the theory of discontinuous dynamical systems, the analytical conditions for chaos synchronization of three different systems are obtained under sinusoidal constraints. With these conditions, the control parameter maps and

Abstract In this paper, based on the original friction-induced oscillation, we propose a new friction-induced mathematical model associated with moving belt of particle supply device. Two delay feedback control methods are provided to make the new model be stable. Linear stability analysis is carried out to obtain the stability of equilibrium and the stability boundary, corresponding to the critical

Abstract Memristor synapse can be used to characterize the electromagnetic induction effect between two neurons that induces an action current by their membrane potential difference. This paper proposes a memristor synapse-coupled neuron network with no equilibrium, which is achieved using a memristor synapse to connect the membrane potentials of two identical three-dimensional memristive Hindmarsh–Rose

Abstract The paper presents work related to nonlinear system parameters identification. The research is focused on systems with hysteretic stiffness characteristics. The identification procedure is developed with use of artificial neural networks. The presented method assumes two separate clusters of neural networks, which are supported by additional signal processing block. Such approach gives an

Abstract This work presents some experimental results for resonant nonlinear response of hyperelastic plates for 1:2 internal resonance. Previously developed topology optimization methods are used to design and fabricate candidate resonant plates using 3-D printing. One such plate is subjected to harmonic transverse excitation with increasing amplitudes in a frequency range where 1:2 internal resonances

Abstract Bolted connections are prone to losing their preloads with the increasing service life, thus inducing engineering accidents and economic losses in industries. Therefore, it is important to detect bolt loosening, while current structural health monitoring methods mainly focus on single-bolt joints, whose applications in industries are limited. Thus, in this paper, a novel vibro-acoustic modulation

Abstract This paper develops an adaptive backstepping optimal control scheme for a fractional-order chaotic magnetic-field electromechanical transducer with the saturated control inputs. A dynamical analysis is used to check for abundant dynamical behaviors of the system by using phase diagrams and time histories under different excitations and fractional orders. A fuzzy wavelet neural network (FWNN)

Abstract In this paper, we study and compare performance and robustness of linear and nonlinear Lanchester dampers. The linear Lanchester damper consists of a small mass attached to a primary system through a linear dashpot, whereas the nonlinear Lanchester damper is linked to the primary mass through dry friction forces. In each case, we propose a semi-analytical method for computing the frequency