Chaos最新文献

In this paper, we propose a novel fourth-order memristive chaotic system (MCS), in which both its dynamical behaviors and the preassigned-time stabilization problem are analyzed. First, the dynamical behaviors of the proposed MCS are studied in detail, such as the infinite unstable equilibrium points, the chaotic attractor, the Lyapunov exponents, the Kaplan-Yorke dimension, and the bifurcation. Then, the T-S fuzzy method is employed to characterize the MCS, and a simpler model is built to deal with the nonlinearity caused by the memristor in the MCS. In addition, two intermittent controllers are proposed to guarantee the preassigned-time stability and the settling time, which can be set freely, independent of system parameters and initial state. Finally, numerical simulations provide solid confirmation for the validity of these theoretical results.

We study three-dimensional diffusive transport of particles through a double-cone channel under stochastic resetting by means of the modified Fick-Jacobs equation. Exact analytical expressions for the unconditional first-passage density and the mean first-passage times in the channel are obtained, and their behavior as a function of the resetting rate is highlighted. Our results show a difference in the mean first-passage times between a narrow-wide-narrow and wide-narrow-wide double-cone geometry. We find in the narrow-wide-narrow double-cone channel with absorbing boundaries a discontinuous transition for the optimal resetting rates, which is not present for the wide-narrow-wide double-cone channel. Furthermore, it is shown how resetting can expedite or slow down the escape of the particle through the double-cone channel. Our results extend the solutions obtained by Jain et al. [J. Chem. Phys. 158, 054113 (2023)].

Investigating the dynamics of neural networks under electromagnetic induction contributes to understanding the complex electrical activity in the brain. This paper proposes a memristive chain Hopfield neural network (MCHNN) containing unidirectional synaptic connections, where a flux-controlled memristor mimics the electromagnetic induction between neurons. Under different parameters, the equilibria of MCHNN have different numbers and properties, thus producing diverse dynamics. Numerical analysis shows that there are diverse coexisting attractors, such as point attractors and periodic and chaotic attractors, which are yielded from different initial conditions. Moreover, the memristor's internal parameter can be considered as a special signal controller. It acts on the oscillation amplitude of the neuron's output signal, along with amplitude control and offset-boosting about the flux. By building a feasible hardware platform, the numerical analysis outcomes are supported, and the existence of the proposed MCHNN is verified. In addition, the NIST test outcomes indicate that MCHNN has good pseudo-randomness and is suitable for engineering applications.

This paper investigates several strategies for modeling electrochemical impedance, in particular, exploring the effects of fractional calculus. It focuses on the theoretical approach for describing systems with anomalous diffusion; as a result, these effects can be analytically expressed as functions of frequency when different boundary conditions are considered. Starting with the normal case as a reference scenario, this study discusses how to increase the complexity of mathematical solutions by generalizing fundamental equations. The second strategy extends the continuity equation to include a fractional contribution. Subsequently, Fick's law is also extended, considering a case that incorporates a fractal derivative. Finally, we utilize electrochemical impedance to determine electric conductivity, analyze mean-square displacement, and connect it to the diffusion process.

Transport through structures such as pores and ion channels is ubiquitous in nature. It has been intensively studied in recent years. Especially in biological cells, the movement of molecules through channel systems plays an essential role in controlling almost every physiological function of living organisms. The subject of our study is the kinetics of spherical particles passing through a conical pore restricted by absorbing and reflecting boundaries from a wider to a narrower end and vice versa. We study the properties of diffusion as a function of particle size with respect to pore width. Particles of different diameters are subjected to a random force. In addition to the mean squared displacement, which indicates the (effective) subdiffusive or superdiffusive character of the motion (depending on whether the absorbing boundary is located at the narrow or wide end of the channel), we measured the mean and median of the first passage times. Additional in silico experiments allowed us to thoroughly discuss the interplay of entropic forces and boundary conditions influencing the obtained results.

Whereas the elastic Hertzian contact force with nonlinear damping gives rise to the overlap dynamics in the discrete element method, the precise physical meaning of tangential springs representing solid friction has remained obscure. Moreover, the well-known difference between the static and the sliding friction coefficient has often been ignored. In the present paper, the recently derived linear continuous spring-dashpot-slider model is generalized for viscoelastic spheres, where the spring stiffness and damping depend on the overlap and its time derivative. It compares favorably to the force-displacement relations obtained from the viscoelastic continuum theory. Both the linear and the generalized, non-linear model readily lend themselves to an efficient implementation of the difference between static and sliding friction coefficients. Their application in a simulation of chute flow quantifies the errors incurred, if one assumes that static and sliding friction coefficients were equal.

Shrimps are islands of regularity within chaotic regimes in bi-parameter spaces of nonlinear dynamical systems. While the presence of periodic shrimps has been extensively reported, recent research has uncovered the existence of quasi-periodic shrimps. Compared to their periodic counterparts, quasi-periodic shrimps require a relatively higher-dimensional phase-space to come into existence and are also quite uncommon to observe. This Focus Issue contribution delves into the existence and intricate dynamics of quasi-periodic shrimps within the parameter space of a discrete-time, three-species food chain model. Through high-resolution stability charts, we unveil the prevalence of quasi-periodic shrimps in the system's unsteady regime. We extensively study the bifurcation characteristics along the two borders of the quasi-periodic shrimp. Our analysis reveals that along the outer border, the system exhibits transition to chaos via intermittency, whereas along the inner border, torus-doubling and torus-bubbling phenomena, accompanied by finite doubling and bubbling cascades, are observed. Another salient aspect of this work is the identification of quasi-periodic accumulation horizon and different quasi-periodic (torus) adding sequences for the self-distribution of infinite cascades of self-similar quasi-periodic shrimps along the horizon in certain parameter space of the system.

In a previous work, we reported cardiac behaviors and, most notably, chaotic arrhythmias of the early afterdepolarization type in the Hindmarsh-Rose model. This behavior appeared to be associated with shrimp-shaped structures in the phase diagram. In this work, we investigate the shrimp region in more detail. We show that shrimps are in fact organized in a spiral pattern known as a hub. Such structures have previously been hypothesized to exist in the Hindmarsh-Rose model but have never been found. Using bifurcation and phase diagrams based on the interspike interval, together with the Lyapunov exponents, we characterize the region of interest. We further clarify the biological behaviors present there and their placement. We use the arrhythmic cardiac behaviors to calculate the corresponding electrocardiogram and interpret its meaning in a clinical setting. We also investigate the movement of the shrimp hub in the parameter space as we change a key parameter of the model. We find evidence that the hub disappears as we decrease the parameter in the direction of one of the most commonly used Hindmarsh-Rose phase diagrams.

Exact reduction by partial integration has been extensively investigated for the Kuramoto model by means of the Watanabe-Strogatz transform. This is the simplest of higher-dimensional reductions that apply to a hierarchy of models in spaces of any dimension, including Riccati systems. Linear fractional transformations enable the system equations to be expressed in an equivalent matrix form, where the variables can be regarded as time-evolution operators. This allows us to perform an exact integration at each node, which reduces the system to a single matrix equation, where the associated time-evolution operator acts over all nodes. This operator has group-theoretical properties, as an element of SU(1,1)∼SO(2,1) for the Kuramoto model, and SO(d,1) for higher-dimensional models on the unit sphere Sd-1. Parameterization of the group elements using subgroup properties leads to a further reduction in the number of equations to be solved and also provides explicit formulas for mappings on the unit sphere, which generalize the Möbius map on S1. Exact dimensional reduction also applies to another class of much less-studied models on the unit sphere, with cubic nonlinearities, for which the governing equations can again be transformed into an equivalent matrix form by means of the unit map. Exact integration at each node proceeds as before, where now the time-evolution operator lies in SL(d,R). The matrix formulation leads to exact solutions in terms of the matrix exponential for trajectories that asymptotically approach fixed points. As examples, we investigate partially integrable models with combined pairwise and higher-order interactions.

Forecasting complex systems is important for understanding and predicting phenomena. Due to the complexity and error sensitivity inherent in these predictive models, forecasting proves challenging. This paper presents a novel approach to assimilate system observations into predictive models. The approach makes use of a recursive partitioning algorithm to facilitate the computation of local sets of model corrections as well as provide a data structure to traverse the model space. These local sets of corrections act as a sample from a piecewise stochastic process. Appending these corrections to the predictive model incorporates hidden residual dynamics, resulting in improved forecasting performance. Numerical experiments demonstrate that this approach results in improved forecasting for the Lorenz 1963 model. In addition, comparisons are made between two types of corrections: Vector Difference and Gaussian. Vector Difference corrections provide the best computational efficiency and forecasting performance. To further justify the effectiveness of this approach it is successfully applied to more complex systems such as Lorenz for various chaotic parameterizations, coupled Lorenz, and cubic Lorenz.