Goldsmedegaard6362

In the present paper, we investigate the impact of time delay during cooperative hunting in a predator-prey model. We consider that cooperative predators do not aggregate in a group instantly, but individuals use different stages and strategies such as tactile, visual, vocal cues, or a suitable combination of these to communicate with each other. We observe that delay in hunting cooperation has stabilizing as well as destabilizing effects in the system. BI-3812 datasheet Also, for an increase in the strength of the delay, the system dynamics switch multiple times and eventually become chaotic. We see that depending on the threshold of time delay, the system may restore its original state or may go far away from its original state and unable to recollect its memory. Furthermore, we explore the dynamics of the system in different bi-parameter spaces and observe that for a particular range of other parameter values, the system dynamics switch multiple times with an increase of delay in all the planes. Different kinds of multistability behaviors, the coexistence of multiple attractors, and interesting changes in the basins of attraction of the system are also observed. We infer that depending on the initial population size and the strength of cooperation delay, the populations can exhibit stable coexistence, oscillating coexistence, or extinction of the predator species.The normal diffusion effect is introduced as a new regulating factor into the established diffusive coupling model for bistable oscillator networks. We find that the response of the system to the weak signal is substantially enhanced by the anormal diffusion, which is termed anormal-diffusion-induced resonance. We also reveal that the diffusive coupling-induced transition, which changes the system from a bistable to a monostable state, is of fundamental importance for the occurrence of resonance. The proposed approach is validated using simulation studies and theoretical analyses. Our results suggest that diffusion induced resonance can be more easily observed in nonlinear oscillator networks.We present numerical results obtained from the modeling of a stochastic, highly connected, and mobile community. The spread of attributes like health and disease among the community members is simulated using cellular automata on a planar two-dimensional surface. With remarkably few assumptions, we are able to predict the future course of propagation of such a disease as a function of time and the fine-tuning of parameters related to interactions among the automata.Photochemical control of the motion of surface active Belousov-Zhabotinsky (BZ) droplets in an oil-surfactant medium is carried out with illumination intensity gradients. Droplet motion is analyzed under conditions of constant uniform illumination and a constant illumination gradient. Control of droplet motion is developed by testing different illumination gradients. Complex hypotrochoid target trajectories are tracked by BZ droplets illuminated with two-dimensional V-shaped gradients.Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be predicted analytically from conservative families of periodic orbits (nonlinear normal modes). However, the stability of forced-damped motions is generally determined a posteriori via numerical simulations. In this paper, we present analytic results on the stability of periodic orbits that perturb from conservative nonlinear normal modes. In contrast with prior approaches to the same problem, our method can tackle strongly nonlinear oscillations, high-order resonances, and arbitrary types of non-conservative forces affecting the system, as we show with specific examples.A Kuramoto-type approach to address flocking phenomena is presented. First, we analyze a simple generalization of the Kuramoto model for interacting active particles, which is able to show the flocking transition (the emergence of coordinated movements in a group of interacting self-propelled agents). In the case of all-to-all interaction, the proposed model reduces to the Kuramoto model for phase synchronization of identical motionless noisy oscillators. In general, the nature of this non-equilibrium phase transition depends on the range of interaction between the particles. Namely, for a small range of interaction, the transition is first order, while for a larger range of interaction, it is a second order transition. Moreover, for larger interaction ranges, the system exhibits the same features as in the case of all-to-all interaction, showing a spatially homogeneous flux when flocking phenomenon has emerged, while for lower interaction ranges, the flocking transition is characterized by cluster formation. We compute the phase diagram of the model, where we distinguish three phases as a function of the range of interaction and the effective coupling strength a disordered phase, a spatially homogeneous flocking phase, and a cluster-flocking phase. Then, we present a general discussion about the applicability of this way of modeling to more realistic and general situations, ending with a brief presentation of a second example (a second model with a conservative interaction) where the flocking transition may be studied within the framework that we are proposing.Anticoordination and chimera states occur in a two-layer model of learning and coordination dynamics in fully connected networks. Learning occurs in the intra-layer networks, while a coordination game is played in the inter-layer network. In this paper, we study the robustness of these states against local effects introduced by the local connectivity of random networks. We identify threshold values for the mean degree of the networks such that below these values, local effects prevent the existence of anticoordination and chimera states found in the fully connected setting. Local effects in the intra-layer learning network are more important than in the inter-layer network in preventing the existence of anticoordination states. The local connectivity of the intra- and inter-layer networks is important to avoid the occurrence of chimera states, but the local effects are stronger in the inter-layer coordination network than in the intra-layer learning network. We also study the effect of local connectivity on the problem of equilibrium selection in the asymmetric coordination game, showing that local effects favor the selection of the Pareto-dominant equilibrium in situations in which the risk-dominant equilibrium is selected in the fully connected network. In this case, again, the important local effects are those associated with the coordination dynamics inter-layer network. Indeed, lower average degree of the network connectivity between layers reduces the probability of achieving the risk-dominant strategy, favoring the Pareto-dominant equilibrium.Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rössler oscillators. The Rössler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.Recent interest in exploiting machine learning for model-free prediction of chaotic systems focused on the time evolution of the dynamical variables of the system as a whole, which include both amplitude and phase. In particular, in the framework based on reservoir computing, the prediction horizon as determined by the largest Lyapunov exponent is often short, typically about five or six Lyapunov times that contain approximately equal number of oscillation cycles of the system. There are situations in the real world where the phase information is important, such as the ups and downs of species populations in ecology, the polarity of a voltage variable in an electronic circuit, and the concentration of certain chemical above or below the average. Using classic chaotic oscillators and a chaotic food-web system from ecology as examples, we demonstrate that reservoir computing can be exploited for long-term prediction of the phase of chaotic oscillators. The typical prediction horizon can be orders of magnitude longer than that with predicting the entire variable, for which we provide a physical understanding. We also demonstrate that a properly designed reservoir computing machine can reliably sense phase synchronization between a pair of coupled chaotic oscillators with implications to the design of the parallel reservoir scheme for predicting large chaotic systems.We investigate the effects of environmental stochastic fluctuations on Kerr optical frequency combs. This spatially extended dynamical system can be accurately studied using the Lugiato-Lefever equation, and we show that when additive noise is accounted for, the correlations of the modal field fluctuations can be determined theoretically. We propose a general theory for the computation of these field fluctuations and correlations, which is successfully compared to numerical simulations.Two paradigmatic nonlinear oscillatory models with parametric excitation are studied. The authors provide theoretical evidence for the appearance of extreme events (EEs) in those systems. First, the authors consider a well-known Liénard type oscillator that shows the emergence of EEs via two bifurcation routes intermittency and period-doubling routes for two different critical values of the excitation frequency. The authors also calculate the return time of two successive EEs, defined as inter-event intervals that follow Poisson-like distribution, confirming the rarity of the events. Further, the total energy of the Liénard oscillator is estimated to explain the mechanism for the development of EEs. Next, the authors confirmed the emergence of EEs in a parametrically excited microelectromechanical system. In this model, EEs occur due to the appearance of a stick-slip bifurcation near the discontinuous boundary of the system. Since the parametric excitation is encountered in several real-world engineering models, like macro- and micromechanical oscillators, the implications of the results presented in this paper are perhaps beneficial to understand the development of EEs in such oscillatory systems.Many spreading processes in our real-life can be considered as a complex contagion, and the linear threshold (LT) model is often applied as a very representative model for this mechanism. Despite its intensive usage, the LT model suffers several limitations in describing the time evolution of the spreading. First, the discrete-time step that captures the speed of the spreading is vaguely defined. Second, the synchronous updating rule makes the nodes infected in batches, which cannot take individual differences into account. Finally, the LT model is incompatible with existing models for the simple contagion. Here, we consider a generalized linear threshold (GLT) model for the continuous-time stochastic complex contagion process that can be efficiently implemented by the Gillespie algorithm. The time in this model has a clear mathematical definition, and the updating order is rigidly defined. We find that the traditional LT model systematically underestimates the spreading speed and the randomness in the spreading sequence order.