Chaos最新文献

Ecological systems can generate striking large-scale spatial patterns through local interactions and migration. In the presence of diffusion and advection, this work examines the formation of flow-induced patterns in a predator-prey system with a Crowley-Martin functional response and prey harvesting, where the advection reflects the unidirectional flow of each species migration (or flow). Primarily, the impact of diffusion and advection rates on the stability and the associated Turing and flow-induced patterns are investigated. The theoretical implication of flow-induced instability caused by population migration, mainly the relative migrations between prey and predator, is examined, and it also shows that Turing instability is the particular condition of flow-induced instability. The influence of the relative flow of both species and prey-harvesting effort on the emerging pattern is reported. Advection impacts a wide range of spatiotemporal patterns, including bands, spots, and a mixture of bands and spots in both harvested and unharvested dynamics. We also observe the diagonally bend-type banded patterns and straight-type banded patterns due to positive and negative relative flows, respectively. Here, the increasing relative flow increases the band length. The growing harvesting effort also decreases the band length, producing a thin band and a mixture of spots and bands due to the negative and positive relative flows, respectively. One exciting result observed here is that harvesting effort drives the flow-Turing and flow-Turing-Hopf instability into pure-flow instability.

Chimeric antigen receptor T (CAR T) cell therapy has been proven to be successful against a variety of leukemias and lymphomas. This paper undertakes an analytical and numerical study of a mathematical model describing the competition of CAR T, leukemia, tumor, and B cells. Considering its significance in sustaining anti-CD19 CAR T-cell stimulation, a B-cell source term is integrated into the model. Through stability and bifurcation analyses, the potential for tumor eradication, contingent on the continuous influx of B cells, has been revealed, showing a transcritical bifurcation at a critical B-cell input. Additionally, an almost heteroclinic cycle between equilibrium points is identified, providing a theoretical basis for understanding disease relapse. Analyzing the oscillatory behavior of the system, the time-dependent dynamics of CAR T cells and leukemic cells can be approximated, shedding light on the impact of initial tumor burden on therapeutic outcomes. In conclusion, the study provides insights into CAR T-cell therapy dynamics for acute lymphoblastic leukemias, offering a theoretical foundation for clinical observations and suggesting avenues for future immunotherapy modeling research.

We consider systems of N particles interacting on the unit circle through 2π-periodic potentials. An example is the N-rotor problem that arises as the classical limit of coupled Josephson junctions and for various energies is known to have a wide range of behaviors such as global chaos and ergodicity, together with families of periodic solutions and transitions from order to chaos. We focus here on selected initial values for generalized systems in which the second order Euler-Lagrange equations reduce to first order equations, which we show by example can describe an ensemble of oscillators with associated emergent phenomena such as synchronization. A specific case is that of the Kuramoto model with well-known synchronization properties. We further demonstrate the relation of these models to field theories in 1+1 dimensions that allow static kink solitons satisfying first order Bogomolny equations, well-known in soliton physics, which correspond to the first order equations of the generalized N-rotor models. For the nonlinear pendulum, for example, the first order equations define the separatrix in the phase portrait of the system and correspond to kink solitons in the sine-Gordon equation.

Signal propagation in biochemical networks is characterized by the inherent randomness in gene expression and fluctuations of the environmental components, commonly known as intrinsic and extrinsic noise, respectively. We present a theoretical framework for noise propagation in a generic two-step cascade (S→X→Y) regarding intrinsic and extrinsic noise. We identify different channels of noise transmission that regulate the individual and the overall noise properties of each component. Our analysis shows that the intrinsic noise of S alleviates the general noise and information transmission capacity along the cascade. On the other hand, the intrinsic noise of X and Y acts as a bottleneck of information transmission. We also show a hierarchical relationship among the intrinsic noise levels of S, X, and Y, with S exhibiting the highest level of intrinsic noise, followed by X and then Y. This hierarchy is preserved within the two-step cascade, facilitating the highest information transmission from S to Y via X.

This paper presents the results of a study of the characteristics of phase synchronization between electrocardiography(ECG) and electroencephalography (EEG) signals during night sleep. Polysomnographic recordings of eight generally healthy subjects and eight patients with obstructive sleep apnea syndrome were selected as experimental data. A feature of this study was the introduction of an instantaneous phase for EEG and ECG signals using a continuous wavelet transform at the heart rate frequency using the concept of time scale synchronization, which eliminated the emergence of asynchronous areas of behavior associated with the "leaving" of the fundamental frequency of the cardiovascular system. Instantaneous phase differences were examined for various pairs of EEG and ECG signals during night sleep, and it was shown that in all cases the phase difference exhibited intermittency. Laminar areas of behavior are intervals of phase synchronization, i.e., phase capture. Turbulent intervals are phase jumps of 2π. Statistical studies of the observed intermittent behavior were carried out, namely, distributions of the duration of laminar sections of behavior were estimated. For all pairs of channels, the duration of laminar phases obeyed an exponential law. Based on the analysis of the movement of the phase trajectory on a rotating plane at the moment of detection of the turbulent phase, it was established that in this case the eyelet intermittency was observed. There was no connection between the statistical characteristics of laminar phase distributions for intermittent behavior and the characteristics of night breathing disorders (apnea syndrome). It was found that changes in statistical characteristics in the phase synchronization of EEG and ECG signals were correlated with blood pressure at the time of signal recording in the subjects, which is an interesting effect that requires further research.

Implementation of logic gates has been investigated in nonlinear dynamical systems from various perspectives over the years. Specifically, logic gates have been implemented in both single nonlinear systems and coupled nonlinear oscillators. The majority of the works in the literature have been done on the evolution of single oscillators into OR/AND or NOR/NAND logic gates. In the present study, we demonstrate the design of logic gates in bi-directionally coupled double-well Duffing oscillators by applying two logic inputs to the drive system alone along with a fixed bias. The nonlinear system, comprising both bi-directional components, exhibits varied logic behaviors within an optimal range of coupling strength. Both attractive and repulsive couplings yield similar and complementary logic behaviors in the first and second oscillators. These couplings play a major role in exhibiting fundamental and universal logic gates in simple nonlinear systems. Under a positive bias, both the first and second oscillators demonstrate OR logic gate for the attractive coupling, while exhibiting OR and NOR logic gates, respectively, for the repulsive coupling. Conversely, under a negative bias, both the first and second oscillators display AND logic gate for the attractive coupling, and AND and NAND logical outputs for the repulsive coupling. Furthermore, we confirm the robustness of the bi-directional oscillators against moderate noise in maintaining the desired logical outputs.

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC-HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size of the linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-like systems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function, and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven model identification algorithms, particularly when applied to commonly used Lorenz time series data.

In this paper, a special spoon neural network is proposed, which is composed of four neurons with direct connection and indirect connection. On this basis, the far induction network and the near induction network (NINN) are constructed by using hyperbolic tangent memristors to explore the influence of electromagnetic induction between neurons at different positions on the dynamic behavior of attractors. NINN exhibits more complex attractor structures and wider chaotic parameters, and also displays a heterogeneous coexisting attractor of limit cycles and chaos under network parameter control. By varying the parameters, coexisting chaotic attractors can be synthesized into a double scrolls attractor, and their oscillation amplitude can be controlled without changing the chaotic characteristics. The type of attractors in human brain determines the clarity of memory. These complex dynamic behaviors demonstrate that near induction has a more pronounced effect on the forgetting and disappearance of memory compared to far induction. Finally, a circuit using switches to change the type of electromagnetic induction is constructed and the results are verified.

Hypernetwork is a useful way to depict multiple connections between nodes, making it an ideal tool for representing complex relationships in network science. In recent years, there has been a marked increase in studies on hypernetworks; however, the comparison of the difference between two hypernetworks has received less attention. This paper proposes a hyper-distance (HD)-based method for comparing hypernetworks. The method is based on higher-order information, i.e, the higher-order distance between nodes and Jensen-Shannon divergence. Experiments carried out on synthetic hypernetworks have shown that HD is capable of distinguishing between hypernetworks generated with different parameters, and it is successful in the classification of hypernetworks. Furthermore, HD outperforms current state-of-the-art baselines to distinguish empirical hypernetworks when hyperedges are randomly perturbed.

As the recent studies indicate, the structure imposed onto written texts by the presence of punctuation develops patterns which reveal certain characteristics of universality. In particular, based on a large collection of classic literary works, it has been evidenced that the distances between consecutive punctuation marks, measured in terms of the number of words, obey the discrete Weibull distribution-a discrete variant of a distribution often used in survival analysis. The present work extends the analysis of punctuation usage patterns to more experimental pieces of world literature. It turns out that the compliance of the the distances between punctuation marks with the discrete Weibull distribution typically applies here as well. However, some of the works by James Joyce are distinct in this regard-in the sense that the tails of the relevant distributions are significantly thicker and, consequently, the corresponding hazard functions are decreasing functions not observed in typical literary texts in prose. Finnegans Wake-the same one to which science owes the word quarks for the most fundamental constituents of matter-is particularly striking in this context. At the same time, in all the studied texts, the sentence lengths-representing the distances between sentence-ending punctuation marks-reveal more freedom and are not constrained by the discrete Weibull distribution. This freedom in some cases translates into long-range nonlinear correlations, which manifest themselves in multifractality. Again, a text particularly spectacular in terms of multifractality is Finnegans Wake.