Chaos最新文献

We study the general periodic motion of a set of three point vortices in the plane, as well as the potentially chaotic motion of one or more tracer particles. While the motion of three vortices is simple in that it can only be periodic, the actual orbits can be surprisingly complex and varied. This rich behavior arises from the existence of both co-linear and equilateral relative equilibria (steady motion in a rotating frame of reference). Here, we start from a general (unsteady) co-linear array with arbitrary vortex circulations. The subsequent motion may take the vortices close to a distinct co-linear relative equilibrium or to an equilateral one. Both equilibrium states are necessarily unstable, as we demonstrate by a linear stability analysis. We go on to study mixing by examining Poincaré sections and finite-time Lyapunov exponents. Both indicate widespread chaotic motion in general, implying that the motion of three vortices efficiently mixes the nearby surrounding fluid outside of small regions surrounding each vortex.

In this paper, we investigate the new generalized stochastic fractional potential-Korteweg-de Vries equation, which describes nonlinear optical solitons and photon propagation in circuits and multicomponent plasmas. Inspired by Kolmogorov-Arnold network and our earlier work, we enhance the improved bilinear neural network method by using a large number of activation functions instead of neurons. This method incorporates the concept of simulating more complicated activation functions with fewer parameters, with more diverse activation functions to generate more complex and rare analytical solutions. On this basis, constraints are introduced into the method, reducing a significant amount of computational workload. We also construct neural network architectures, such as "2-3-1," "2-2-3-1," "2-3-3-1," and "2-3-2-1" using this method. Maple software is employed to obtain many exact analytical solutions by selecting appropriate parameters, such as the superposition of double-period lump solutions, lump-rogue wave solutions, and three interaction solutions. The results show that these solutions exhibit more complex waveforms than those obtained by conventional methods, which is of great significance for the electrical systems and multicomponent fluids to which the equation is applied. This novel method shows significant advantages when applied to fractional-order equations and is expected to be increasingly widely used in the study of nonlinear partial differential equations.

Exploring spatiotemporal patterns of high-dimensional electroencephalography (EEG) time series generated from complex brain system is crucial for deciphering aging and cognitive functioning. Analyzing high-dimensional EEG series poses challenges, particularly when employing distance-based methods for spatiotemporal dynamics. Therefore, we proposed an innovative methodology for multi-channel EEG data, termed as Spatiotemporal Information-based Similarity (STIBS) analysis. The core of this method is to first perform state space compression of multi-channel EEG time series using global field power, which can provide insight into the dynamic integration of spatiotemporal patterns between the steady states and non-steady states of brain. Subsequently, we quantify the pairwise differences and non-randomness of spatiotemporal patterns using an information-based similarity analysis. Results demonstrated that this method holds the potential to serve as a distinguishing marker between young and elderly on both pairwise differences and non-randomness indices. Young individuals and those with higher cognitive abilities exhibit more complex macrostructure and non-random spatiotemporal patterns, whereas both aging and cognitive decline lead to more randomized spatiotemporal patterns. We further extended the proposed analytics to brain regions adversarial STIBS (bra-STIBS), highlighting differences between young and elderly, as well as high and low cognitive groups. Furthermore, utilizing the STIBS-based XGBoost model yields superior recognition accuracy in aging (93.05%) and cognitive functioning (74.29%, 64.19%, and 80.28%, respectively, for attention, memory, and compatibility performance recognition). STIBS-based methodology not only contributes to the ongoing exploration of neurobiological changes in aging but also provides a powerful tool for characterizing the spatiotemporal nonlinear dynamics of the brain and their implications for cognitive functioning.

A deep understanding of non-smooth dynamics of vehicle systems, particularly with dry friction damping offer valuable insights into the design and optimization of railway vehicle systems, ultimately enhancing the safety and reliability of railway operations. In this paper, the two-parameter dynamics of a non-smooth railway wheelset system incorporating dry friction damping are investigated. The effect of the crucial parameters on the complexity of the evolution process is comprehensively exposed by identifying different dynamic responses in the two-parameter plane. In addition, the multistability and the various routes transition to chaos for the system are also discussed. It is found that dry friction induces highly complex dynamics in the system, encompassing a range of behaviors such as periodic, quasi-periodic, and chaotic motions. These intricate dynamics are a direct result of the interplay between multiple parameters, such as speed and damping coefficients, which are critical in determining the system's stability and performance. The presence of multistability further complicates the system, resulting in unpredictable transitions between different motion states.

In this paper, a Caputo fractional tumor immune model of combination therapy is established. First, the stability and biological significance of each equilibrium point are analyzed, and it is demonstrated that chaos may arise under specific conditions. Combined with the mathematical definition of Caputo fractional differentiation (CFD), it is found that there is a high correlation between the chaotic phenomenon of the patient's condition and the sensitivity of the patient to the change in the state of the day. The bifurcation threshold of each parameter is determined through numerical simulation, and the Hopf bifurcation of direct competition coefficient and inhibition coefficient between tumor cells and host healthy cells is elaborated upon in detail. Subsequently, a novel method combining optimal control theory with the particle swarm optimization (PSO) algorithm is proposed for the optimal control of the tumor immune model in combination therapy. Finally, the Adams-Bashforth-Moulton (ABM) prediction correction method is utilized in numerical simulations which demonstrate that the introduction of the CFD alters the model dynamics. Furthermore, these results indicate that fractional calculus can effectively be applied to tumor immune models better to elucidate complex chaotic dynamics of tumor cell evolution. Concurrently, the PSO can be successfully integrated with optimal control theory to address optimization challenges in cancer treatment.

Coffee leaf rust is a prevalent botanical disease that causes a worldwide reduction in coffee supply and its quality, leading to immense economic losses. While several pandemic intervention policies (PIPs) for tackling this rust pandemic are commercially available, they seem to provide only partial epidemiological relief for farmers. In this work, we develop a high-resolution spatiotemporal economical-epidemiological model, extending the Susceptible-Infected-Removed model, that captures the rust pandemic's spread in coffee tree farms and its associated economic impact. Through extensive simulations for the case of Colombia, a country that consists mostly of small-size coffee farms and is the second-largest coffee producer in the world, our results show that it is economically impractical to sustain any profit without directly tackling the rust pandemic. Furthermore, even in the hypothetical case where farmers perfectly know their farm's epidemiological state and the weather in advance, any rust pandemic-related efforts can only amount to a limited profit of roughly 4% on investment. In the more realistic case, any rust pandemic-related efforts are expected to result in economic losses, indicating that major disturbances in the coffee market are anticipated.

A beautiful feature of nature is its complexity. The chaos theory has proved useful in a variety of fields, including physics, chemistry, biology, and economics. In the present article, we explore the complex dynamics of a rather simple one-dimensional economic model in a parameter plane. We find several organized zones of "chaos and non-chaos" and different routes to chaos in this model. The study reveals that even this one-dimensional model can generate intriguing shrimp-shaped structures immersed within the chaotic regime of the parameter plane. We also observe shrimp-induced period-bubbling phenomenon, three times self-similarity of shrimp-shaped structures, and a variety of bistable behaviors. The emergence of shrimp-shaped structures in chaotic regimes can enable us to achieve favorable economic scenarios (periodic) from unfavorable ones (chaotic) by adjusting either one or both of the control parameters over broad regions of these structures. Moreover, our results suggest that depending on the parameters and initial conditions, a company may go bankrupt, or its capital may rise or fall in a regular or irregular manner.

In epidemic networks, it has been demonstrated that implementing any intervention strategy on nodes with specific characteristics (such as a high degree or node betweenness) substantially diminishes the outbreak size. We extend this finding with a disease-spreading meta-population model using testkits to explore the influence of migration on infection dynamics within the distinct communities of the network. Notably, we observe that nodes equipped with testkits and no testkits tend to segregate into two separate clusters when migration is low, but above a critical migration rate, they coalesce into one single cluster. Based on this clustering phenomenon, we develop a reduced model and validate the emergent clustering behavior through comprehensive simulations. We observe this property in both homogeneous and heterogeneous networks.

Third-party intervention is a beneficial means to alleviate conflicts and promote cooperation among disputants. The decision-making of disputants is closely related to the intensity of the impact of third-party intervention on their profits. Actually, disputants often decide whether to adopt cooperative strategies based on their own perceived rather than actual gains or losses brought about by third-party intervention. We, therefore, introduce prospect theory to explore the formation and maintenance of cooperation in a system composed of third parties and disputants, which, respectively, constitute two sub-networks of the interdependent networks. Both interveners and disputants participate in a prisoner's dilemma game, and the third-party intervener will pay a certain price to impose certain punishments on the defectors of the disputed layer. The simulation results show that the introduction of third-party intervention based on the prospect theory alleviates the conflicts in the dispute layer and promotes cooperation among disputants, which indicates that third parties such as governments or organizations should appropriately consider the risk attitudes of disputants when mediating their conflicts. The level of cooperation at the dispute layer is inversely proportional to the intervention cost and directly proportional to the intervention intensity. Our research may shed some new light on the study of the evolution of cooperation under third-party intervention.

An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis into 2D. It is tested on synthetic structures to ensure its effectiveness, with results indicating consistency. The interdisciplinary potential of this method in describing real surfaces and images is demonstrated, revealing previously unknown directional multifractality in data sets from the Martian surface and the Crab Nebula. The multifractal characteristics of Jackson Pollock's paintings are also analyzed. The results point to their evolution over the time of creation of these works.