Abstract: Abstract Many mechanical systems exhibit destabilization of a single mode as some parameters are varied. In such situations, the destabilizing effect is often modeled using a negative damping term, e.g., in flow induced galloping instability of a pipe in a cross-flow. A small, nonlinear, not precisely tuned, lightly damped, secondary system mounted on the primary system can stabilize the primary system over some useful range of parameter values. We study such a system, modeling the primary system as a linear, negatively damped, single-degree-of-freedom oscillator and modeling the small secondary system using small linear damping and significantly nonlinear stiffness. Numerical simulations show useful behavior over a range of parameters even without precise tuning of the secondary system. Analytical treatment using harmonic balance followed by an informal averaging calculation yields amplitude and phase equations that capture the dynamics accurately over a range of parameters. Although intermediate expressions involved are long and unwieldy, numerical and analytical treatment of the equations lead to simplifying insights which in turn allow us to construct useful approximate formulas that can be used by practitioners. In particular, simple approximate expressions are obtained for oscillation amplitudes of the primary and secondary systems and for the negative damping range over which effective vibration stabilization occurs, in terms of system parameters. PubDate: 2021-01-19

Abstract: Abstract The position-dependent non-conservative forces are called curl forces introduced recently by Berry and Shukla (J Phys A 45:305201, 2012). The aim of this paper is to study mainly the curl force dynamics of non-conservative central force \(\ddot{x} = -xg(x,y)\) and \(\ddot{y} = -yg(x,y)\) connected to higher-order saddle potentials. In particular, we study the dynamics of the type \(\ddot{x}_i = -x_ig \big (\frac{1}{2}(x_{1}^{2} - x_{2}^{2}) \big )\) , \(i=1,2\) and its application towards the trapping of ions. We also study the higher-order saddle surfaces, using the pair of higher-order saddle surfaces and rotated saddle surfaces by constructing a generalized rotating shaft equation. The complex curl force can also be constructed by using this pair. By the direct computation, we show that all these motions of higher-order saddles are completely integrable due to the existence of two conserved quantities, viz. energy function and the Fradkin tensor. The Newtonian system \(\ddot{x} = {{\mathcal {X}}}(x,y)\) , \(\ddot{y} = {{\mathcal {Y}}}(x,y)\) has also been studied with an energy like first integral \(I(\mathbf{x}, \dot{\mathbf{x}}) = \frac{1}{2}\dot{\mathbf{x}}^TM(\mathbf{x})\dot{\mathbf{x}} + U(\mathbf{x})\) , where \(M(\mathbf{x})\) is a \((2 \times 2)\) matrix of which the components are polynomials of degree less than or equal to two and the condition on \({{\mathcal {X}}}\) and \({{\mathcal {Y}}}\) for which the curl is non-vanishing is also obtained. PubDate: 2021-01-19

Abstract: Abstract This paper considers a robust resource allocation strategy design problem in technology innovation ecosystem. The purpose is for both healthy competition and symbiosis between populations. We formulated this as a control design problem. There are three salient features of this problem. First, the control, since it means the resource and should always be positive, is constrained. Second, the state, since it means the population and should always be positive, is constrained. Third, the system, since it represents the interactions between the societal biomass and the resources, is highly uncertain. We endeavor to propose two separate transformations on the state and the control to convert the system to an equivalent and unconstrained system. In a sense, we embed the constraints into the (nonlinear) intrinsic system structure. Following this, the control design has to address two issues. First, the control is to render desirable performance of this (constraint-embedded) system regardless of the uncertainty. Second, the performance of the original system, which is the primary concern, should be equally within the threshold. This paper should be the first effort that addresses the resource allocation strategy of technology innovation ecosystem from the control perspective. PubDate: 2021-01-19

Abstract: Abstract In this article, the issue of dissipative asynchronous control for continuous-time T–S fuzzy singular Markov jump linear parameter-varying systems against dual deception attacks under the dynamic event-triggered transmission protocol (DETP) is investigated. Firstly, the DETP is offered to further abate the channel congestion caused by the limited bandwidth. Meanwhile, the mutually independent random variables subject to Bernoulli distribution are utilized to model the dual deception attacks, which can destroy the integrity of the considered system to some degree. Besides, since the controller can not accurately receive the system information, a hidden Markov model is established to depict the asynchronous phenomenon. Specifically, in the light of the parameter-dependent Lyapunov functional, the stochastic admissible criterion of the closed-loop system with certain dissipative performance and uncertain transition rates is obtained. Ulteriorly, based on the parameter-dependent linear matrix inequalities, a cooperative design technique of asynchronous controller and the weighting matrix of the DETP is proposed. Finally, two examples of chaotic systems and electric truck-trailer systems under the DETP are given to illustrate the feasibility of the proposed method. PubDate: 2021-01-18

Abstract: Abstract The mathematical model with time delay is often more practical because it is subject to current and past state. What remains unclear are the details, such as how time delay and sudden environmental changes influence the dynamic behavior of systems. The purpose of this paper is to analyze the long-time behavior of a stochastic Nicholson’s blowflies model, which includes distributed delay and degenerate diffusion. The application of the Markov semigroups theory is to prove that there exists a unique stationary distribution. What’s more, the expression of probability density function around the unique positive equilibrium of the deterministic model is briefly described under a certain condition. The results of this paper can be used to find that the weaker white noise can guarantee the existence of a unique stationary distribution and the stronger mortality rate can cause the extinction of Nicholson’s blowflies. Some numerical examples are also given to explain the effect of the white noise. PubDate: 2021-01-17

Abstract: Abstract It is well known that most of real-world phenomena are described by partial differential equations. Nevertheless, for control design purposes it is very common to approximate them with a set of ordinary differential equations, since conventional design methods, such as calculus of variations or differential geometry, turn out to be very complex for this class of systems. However, by doing this, valuable properties are lost. In this work, we present a dynamical distributed control for nonlinear partial differential equation systems and we focus on solving the Generalized Synchronization problem, since this topic has multiple applications in the disciplines of engineering, biology, physics, etc. For the design of the control, we utilize a differential algebraic approach. The key ingredient of our design method is to find a canonical form of the given systems by means of the so-called partial differential primitive element. This representation is known as Generalized Observability Canonical Form and allows us to design a dynamical distributed control in a natural way. Additionally, to avoid a functional analysis for the stability of the resultant synchronization error, we propose to utilize tools from semi-group and spectral theory of infinite dimensional systems in a Hilbert space. As a result, we present a design approach less complex and, therefore, more accessible than most common design methods. Besides, with the proposed stability analysis, we obtain an easy criterion to select the control gains; hence, we can solve the generalized synchronization problem of partial differential equation systems in a simple way. To validate the effectiveness of the proposed control, we present two examples of generalized synchronization for reaction-diffusion systems and show their respective numerical results. PubDate: 2021-01-16

Abstract: Abstract In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations. PubDate: 2021-01-16

Abstract: Abstract The paper develops an approximate solution to the system of Euler’s equations with additional perturbation term for dynamically symmetric rotating rigid body. The perturbed motions of a rigid body, close to Lagrange’s case, under the action of restoring and perturbation torques that are slowly varying in time are investigated. We describe an averaging procedure for slow variables of a rigid body perturbed motion, similar to Lagrange top. Conditions for the possibility of averaging the equations of motion with respect to the nutation phase angle are presented. The averaging technique reduces the system order from 6 to 3 and does not contain fast oscillations. An example of motion of the body using linearly dissipative torques is worked out to demonstrate the use of general equations. The numerical integration of the averaged system of equations is conducted of the body motion. The graphical presentations of the solutions are represented and discussed. A new class of rotations of a dynamically symmetric rigid body about a fixed point with account for a nonstationary perturbation torque, as well as for a restoring torque that slowly varies with time, is studied. The main objective of this paper is to extend the previous results for problem of the dynamic motion of a symmetric rigid body subjected to perturbation and restoring torques. The proposed averaging method is implemented to receive the averaging system of equations of motion. The graphical representations of the solutions are presented and discussed. The attained results are a generalization of our former works where µ and Mi are independent of the slow time τ and Mi depend on the slow time only. PubDate: 2021-01-16

Abstract: Abstract A family of mem-models, including the mem-dashpots, mem-springs, and most recently, mem-inerters, is emerging as a new and powerful way of capturing complex nonlinear behaviors of materials and systems under various types of dynamic loads involving different frequency, amplitude, and loading histories (e.g., hysteresis). Under the framework of nonlinear state-space representation and hybrid dynamical systems, mem-springs may be formulated to effectively represent an inherent degradation of material state. It is shown in this study, for the first time, how the absement (time integral of strain/displacement), a signature state variable for a mem-spring, can be connected with the damage variable, a key quantity in continuum damage mechanics. The generalized momentum (time integral of stress), on the other hand, is shown to be efficient in modeling strain ratcheting via the concept of mem-dashpot. It is also shown in this study, for the first time, how two formulations of the memcapacitive system models (for mem-springs) are special cases of the Preisach model. PubDate: 2021-01-16

Abstract: Abstract In this Comment, we correct misprints in equations of the paper “Fractional Nonlinear Dynamics of Learning with Memory” Nonlinear Dynamics. 2020. Vol.100. P.1231–1242. We also give conditions of the existence of solutions for nonlinear fractional differential equation, which correct the conditions given in Propositions 3.8 and 3.9 of the book (Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006). These conditions impose restrictions on the existence of solutions of nonlinear equations that describe the dynamics of learning with memory. Using these conditions, we give the correct formulations of the principle of inevitability of growth for process with memory and the principle of changing growth rates by memory, which are proposed in the commented article. PubDate: 2021-01-15

Abstract: Abstract Conventional neural networks are universal function approximators, but they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here, we prepend a conventional neural network to a Hamiltonian neural network and show that the combination accurately forecasts Hamiltonian dynamics from generalised noncanonical coordinates. Examples include a predator–prey competition model where the canonical coordinates are nonlinear functions of the predator and prey populations, an elastic pendulum characterised by nontrivial coupling of radial and angular motion, a double pendulum each of whose canonical momenta are intricate nonlinear combinations of angular positions and velocities, and real-world video of a compound pendulum clock. PubDate: 2021-01-15

Abstract: Abstract In this article, the effects of the changes in the mass of the floating wind turbine (as a multi-body system) on its nonlinear vertical vibrations are investigated. The fluctuations of the hydrodynamic added mass of the floating platform and the mass of the vibration absorbers, which added to the structure to mitigate the lateral vibrations, change the mass and consequently the dynamics of the vertical vibrations. In this regard, first, the governing equations of the vertical vibrations of the floating wind turbine are derived. The FAST code is used to validate the proposed model of the dynamics of the vertical vibrations through numerical simulations. Then, derived equations are solved approximately by the perturbation method. According to the approximate solutions, the fluctuations of the added mass of the floating platform and the masses of the vibration absorbers increase the frequency and amplitude of the vertical vibrations, which increases the fatigue loads on the tower of the wind turbine as well as moorings of the floating platform. PubDate: 2021-01-14

Abstract: Abstract Nowadays, scientists are increasingly asked to investigate problems, which require the analysis of irregular, chaotic, non-stationary and corrupted time series. Assessing the causal relations between such signals is particularly challenging and, in many instances, interventions and experiments are impossible or impractical. The present work is a contribution to the development of indicators to quantify the mutual influences between time series. The criterion is called Cross Markov Matrix and belongs to the strand of techniques based on the conversion of time series into complex networks and the subsequent analysis of their topological properties. The proposed indicator is quite competitive with the available tools and can complement them very effectively. Indeed, all techniques have their strong and weak points and therefore corroborating the conclusions with mathematically independent methods is a recommended practice. The properties of the Cross Markov Matrix have been investigated with the help of a systematic series of numerical tests using synthetic data. The potential of the approach is then substantiated by the analysis of various real-life examples, ranging from environmental and global climate problems to the mutual influence between media coverage of Brexit and the pound-euro exchange rate. PubDate: 2021-01-13

Abstract: Abstract The proposed observer-based control mechanism solves the trajectory tracking problem in the presence of external disturbances with the reduction in sensor numbers. This systematically considers the quadcopter nonlinear dynamics and parameter and load variations by adopting the standard controller design approach based on a disturbance observer (DOB). The first feature is designing first-order observers for estimating the velocity and angular velocity error, with their parameter independence obtained from the DOB design technique. As the second feature, the resultant velocity observer-based control action including active damping and DOBs secures first-order tracking behavior for the position and attitude (angle) loops through pole zero cancellation, thereby forming a proportional–derivative control structure. Closed-loop analysis results reveal the performance recovery and steady-state error removal properties in the absence of tracking error integrators. The numerical verification confirms the effectiveness of the proposed mechanism using MATLAB/Simulink. PubDate: 2021-01-13

Abstract: Abstract At present, the main measures for disease control are vaccination, quarantine and treatment. Taking the three measures into consideration, time-varying optimal control problems of an SIQS epidemic model of the network are proposed, and the aim of this paper is to reduce control costs. The existence and solutions of the problems are solved by the optimal control theory. At last, the theoretical results are illustrated by numerical simulations. The results of numerical simulations show the advantages of different control strategies. It may be helpful for the development of disease control strategies. Our results are suitable for diseases in which a recovered individual may have lost immunity and can be infected again. PubDate: 2021-01-13

Abstract: Abstract With the development of vehicle technology, the number of vehicles equipped with the adaptive cruise control (ACC) system is increasing, and it is more and more common for ACC vehicles to drive with regular vehicles. In this work, we proposed a mixed traffic model with regular vehicles and ACC vehicles via the transformation of micro-model and macro-model. The linear stability analysis tells that the permeability of ACC vehicles has an important influence on the traffic system. Meanwhile, through the nonlinear analysis, the KdV–Burgers equation describing the density wave is obtained. Besides, the results of numerical simulations are consistent with the theory, which indicates that the increase in ACC vehicles is conducive to the stability of the transportation system. PubDate: 2021-01-12

Abstract: Abstract An active suspension of an intelligent electric vehicle driven by four in-wheel motors (IEV-DFIM) is a strong nonlinear system because of time-varying parameters in practice, which causes difficult controllability. For addressing this issue, the paper proposes a novel homogeneous output feedback control method. Firstly, an active suspension dynamic model which considers the time-varying sprung mass, stiffness coefficients and damping coefficients is built. Secondly, an active suspension control system is constructed based on the dynamic model whose uncertain and nonlinear terms do not meet the linear or high-order growing. Thirdly, the homogeneous output feedback method is developed to relax the growth condition imposed on the uncertain and nonlinear terms for the active suspension. Finally, the simulation and test are carried out to verify the effectiveness of the designed controller compared with the sliding mode control method and passive suspension. PubDate: 2021-01-12

Abstract: Abstract This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme. PubDate: 2021-01-12

Abstract: Abstract A generalized Nicholson blowflies model with harvesting or immigration and random effect is considered. We discuss the existence of positive global solution and provide the estimate on the lower bound of the Lyapunov exponent. Moreover, we show that the nontrivial equilibrium solution is mean square exponential stability and stable in probability. We prove several results using techniques of stochastic calculus. It is evident from the obtained conditions that the noise plays an important role in all qualitative properties of the solution. Numerical simulations are also provided in order to validate the analytical findings. The results are new and compliments the existing ones. PubDate: 2021-01-11

Abstract: Abstract The current push toward lightweight structures in aerospace and aeronautical engineering is leading to slender design airfoils, which are more likely to undergo large deformation, hence experiencing geometrical nonlinearities. The problem of vibration localization in a rotor constituted by N coupled airfoils with plunge and pitch degrees of freedom subjected to flutter instability is considered. For a single airfoil, it is shown that depending on the system parameters, multiple static and dynamic equilibria coexist which may be a fixed point, a limit cycle, or irregular motion. By elastically coupling N airfoils, a simplified rotor model is obtained. The nonlinear dynamical response of the rotor is studied via time integration with particular attention to the emergence of localized vibrating solutions, which have been classified introducing a localization coefficient. Finally, the concept of basin stability is exploited to ascertain the likelihood of the system to converge to a certain localized state as a function of the airstream velocity. We found that homogeneous and slightly localized states are more likely to appear with respect to strongly localized states. PubDate: 2021-01-11