Communications in Nonlinear Science and Numerical Simulation最新文献

The cell membrane has a layered structure, which separates the intracellular and extracellular ions for developing gradient electromagnetic field, and its flexible property enables the capacitance dependence on the shape deformation due to external stimuli. Therefore, piezoelectric membrane can be suitable to describe the biophysical characteristic of cell membrane and equivalent circuit approach becomes important. In this paper, two capacitors are connected via a piezoelectric ceramic and two additive memristive channels are combined to mimic the neural activity response with exact energy description. Furthermore, linear transformation is applied to obtain an equivalent piezoelectric map neuron and energy function is provided to explore the adaptive energy regulation on mode selection in neural activities. Coherence resonance is detected and analyzed. The map neuron can also be considered as an auditory neuron for perceiving acoustic signals and its membrane property is considered from physical aspect.

The stochastic optimization of a nonlinear energy sink (NES) with a time-dependent stiffness is considered. The NES is linearly coupled to a main system. The optimization aims to find the stiffness properties of the NES that minimize the expected value of the velocity of the main system while accounting for the statistical distributions of the excitation amplitude and frequency. It is shown that the system’s responses are highly sensitive to uncertainty and can even exhibit a discontinuous behavior. This represents a major hurdle for the optimization, which is already hampered by the potentially large computational cost associated with the time integrations. To tackle the high-sensitivity to uncertainties and reduce the computational burden, a dedicated surrogate-based stochastic optimization algorithm is used. Specifically, the approach uses Kriging surrogates built from the unsupervised identification of clusters resulting from response discontinuities. Comparisons between efficiencies of optimal nonlinear absorbers with and without time-dependent stiffness are performed and discussed.

This paper investigates the problem of finite time prescribed performance control (PPC) for a number of nonlinear stochastic systems with asymmetric error constraint, unknown control directions, and actuator faults. Firstly, instead of introducing the performance constraint function in the Lyapunov function, a new asymmetric error conversion function (AECF) is presented, which can successfully constrain the tracking errors into the specified asymmetric boundaries and eliminate the feasibility condition of requiring tracking errors to be bounded. Then, in iterative process, the unknown intermediate virtual controller is approximated by the fuzzy logic system (FLS), which makes each actual virtual controller to be reduced to only one item. Furthermore, the investigated finite time PPC strategy can fully compensate the faults impact on the systems and have only one adaptive parameter. In the end, the efficacy of investigated strategy is verified by inverted pendulum systems with stochastic disturbances.

This article addresses the challenge of achieving practically fast finite-time stabilization for stochastic constrained nonlinear systems, which are subject to both quantization effects and actuator dead zones. To tackle these issues, adaptive parameterization and partial control strategies are introduced with the aim of efficiently approximating and counteracting nonlinear disturbances. This approach ensures the robust stabilization of the controlled system within a finite time frame, despite the presence of uncertainties. Additionally, a novel barrier function is propose that mitigates the constraints usually imposed by boundary functions, while also leveraging a fuzzy logic system to manage nonlinear terms adeptly. Building on these innovations, we formulate a new theorem dedicated to practically fast finite-time control mechanisms for stochastic nonlinear systems. The efficacy of our theoretical developments is substantiated through an illustrative example involving a current-controlled DC motor system, demonstrating the practical applicability and robustness of the proposed control scheme.

In this article, a kind of second-order neural networks with variable coefficients and distributed delays are discussed. At first, new lemmas about fixed/preassigned-time synchronization for such system are respectively constructed. Then, some novel criteria are given to get fixed/preassigned-time synchronization for such delayed system based on the these lemmas. Unlike feedback controllers are used in previous works, two effective event-triggered controllers are, respectively, proposed here to investigate the second-order neural networks. In addition, event-triggered control and non-reduced order way are combined use to realize fixed/preassigned-time synchronization for such delayed system at the first time, which has advantages from both efficiency of control and brevity of criterion. Finally, two examples are presented to show validity of the proposed criteria.

Due to the existence of gaps or backlash, many mechanical systems can be simplified into piecewise linear models. The dynamic study on mechanical systems should be based on reliable mathematical models. So that it is very important to determine the contact point and separation point between the primary system and the auxiliary spring system (ASS) in a piecewise linear system. In most existing literature, the contact point and separation point of the mathematical model are fixed at the gap. But in this paper, it is found that the contact point and separation point actually change with the system parameters when the ASS contains a damper, which implies the most existing mathematical models are incorrect. It is firstly demonstrated through numerical solution that the primary system will prematurely separate from the ASS before reaching the gap under harmonic excitation, which shows the incorrectness of the classical mathematical models. Then, based on the mechanical model and engineering practice, two corrected mathematical models are proposed. And the motions of the primary system and ASS after premature separation in the corrected models are studied. Finally, through comparisons of the contact points, separation points, amplitude-frequency curves and motion states between the corrected models and the classical mathematical model, it can be concluded that the corrected models are more reasonable. And comparisons with the experimental data imply that the corrected models can better reflect the engineering practice. These results will be helpful to the study and design of the piecewise linear system.

In this article, we explore the general decay anti-synchronization (GDAS) and general decay $H_{\infty }$ anti-synchronization (GDHAS) of derivative coupled delayed memristive neural networks (DCDMNNs) with constant and delayed state coupling, respectively. To begin with, on account of the definitions of $\psi$-type function as well as $\psi$-type stability, we present the GDAS and GDHAS concepts for the considered DCDMNNs. What is more, several sufficient conditions are derived for reaching GDAS and GDHAS of DCDMNNs with constant and delayed state coupling by selecting correct Lyapunov functionals and devising a proper controller. Moreover, numerical simulations examples are provided to demonstrate the feasibility of the obtained conclusions.

This paper considers a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay. The spatio-temporal delay is modeled as the convolution of $u(t,x)$ with a kernel function $g(t,x)\ge 0$, where ${\int }_R{\int }_0^{+\infty }g(s,y)dsdy=1$. By constructing an auxiliary system, applying Schauder’s fixed point theorem, and using a limiting argument, we demonstrate that the model admits non-negative traveling wave solutions connecting the equilibrium $(0,0)$ to some unknown positive steady states (also referred to as a semi-wavefront) when the wave speed satisfies $c\ge c^{\ast }=2\sqrt{1-r}$. Moreover, no such semi-wavefront exists if $c<c^{\ast }$. It is noteworthy that the kernel function is not required to have compact support in this analysis.

In this paper, we deal with numerical approximations for solving the Black–Scholes Partial Differential Equation (PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally of both stock price and time. In contrast to constant volatility or time-dependent volatility models for which analytical representations of the exact solution is known for European Call options, there is no analytical solution for local volatility. The space discretization is performed using the classical finite volume method with Two-Point Flux Approximation (TPFA) and a novel scheme called Fitted Two-Point Flux Approximation (FTPFA). The Fitted Two-Point Flux Approximation (FTPFA) combines the fitted finite volume method and the standard TPFA method. More precisely the fitted finite volume method is used when the stock price approaches zero with the goal to handle the degeneracy of the PDE while the TPFA method is used on the rest of space domain. This combination yields our fitted TPFA scheme. The Euler method is used for the time discretization. We provide the rigorous convergence proofs of the two fully discretized schemes. Numerical experiments to support theoretical results are provided.

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely ($\alpha \eta$)-contractive type covariant mappings and contravariant mappings, and ($\beta \chi$)-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for ($\alpha \eta$)-contractive type covariant mappings and contravariant mappings, and for ($\beta \chi$)-contractive type covariant mappings in complete fuzzy bipolar metric spaces utilizing the triangular property. Additionally, to substantiate the findings, some illustrative examples and consequential outcomes are presented. Furthermore, the proven results serve to extend, generalize, and enhance the corresponding outcomes documented in existing literature. A practical application of these findings in the context of non-linear Volterra integral equations is demonstrated, solidifying and reinforcing the credibility of the established results. Overall, this paper contributes to the understanding of fixed point theory in the context of fuzzy bipolar metric spaces and highlights the significance of ($\alpha \eta$)-contractive mappings and ($\beta \chi$)-contractive mappings in this domain.