Physica D: Nonlinear Phenomena最新文献

In this manuscript, an attempt has been made to understand the delay induced (gestation and carry-over effect delay) dynamics of an ecological system with generalist predator exerted fear and its carry-over effect with competitive interference. The designed model exhibits finite time blow up depending on large initial data. The stability of both the delayed and non-delayed systems have been analyzed along with Hopf-bifurcation analysis. It has been observed that carry-over and fear effects act in opposite way in context of stability control for non-delayed system. The two delay (carry-over effect and gestation delay) have significant impact on the dynamics. The former exhibits both stabilizing and destabilizing role while the latter has a destabilizing tendency on the system dynamics. The blow up phenomena for predator species have been shown numerically by verifying the analytical conditions. Our study incorporates a diverse array of figures and diagrams to illustrate and support our findings. Through the exploration of non-linear models, our research unveils several intriguing characteristics. These insights can prove invaluable for biologists seeking a more detailed and pragmatic understanding of generalist predator–prey systems. The visual representations provided in our study contribute to a comprehensive analysis, enhancing the accessibility and applicability of the findings for researchers and practitioners in the field.

The honeybee has a significant impact on ecosystem stability, biodiversity conservation, and pollinating crops. However, during the past few years, there has been a sharp reduction in both the honeybee population and their colonies. It has been found that the parasitic mite Varroa destructor is responsible for the decline in honeybee colonies around the world, which in turn immensely affects the economic growth of a country. To investigate how the dynamics of a system is influenced by the growth of honeybees and the parasitism of mites, we study a nonlinear honeybee-mite population model in a discrete-time setup. We observe that an increase in the value of the queen’s egg-laying rate drives the system towards chaos. However, chaos can be controlled as well if the parasite attachment effect is increased. The intrinsic dynamical properties of the proposed system are investigated with the simultaneous variation of the queen’s egg-laying rate and the mite’s parasite attachment effect by constructing several largest Lyapunov exponent and isoperiodic diagrams. The investigation reveals the existence of several periodic structures in the quasiperiodic and chaotic regimes of the parameter plane, including Arnold tongues, saddle area, spring area, connected shrimp-shaped structure, and connected saddle area. We also find the appearance of a novel ‘jellyfish’-shaped periodic structure. One of the most fascinating findings of this study is the appearance of Arnold tongues along the inner boundary region of another Arnold tongue. In addition, this work also reveals different types of multistability, e.g., the coexistence of two, three, and even four attractors. What is more interesting is that the current analysis unveils the coexistence of five attractors as well, more specifically, four different periodic attractors coexist with the trivial fixed point attractor, which is quite rare in ecological systems. The structures of the basins of these coexisting attractors are either smooth or very complex in nature. Furthermore, the present study also discloses the fact that variation in the initial condition of the system can significantly change the appearance of the periodic structures in the parameter plane.

In this paper, the spatiotemporal dynamics and pattern formation of a space–time discrete intraguild predation model with self-diffusion are investigated. The model is obtained by applying a coupled map lattice (CML) method. First, using linear stability analysis, the existence and stability conditions for fixed points are determined. Second, using the center manifold theorem and the bifurcation theory, the occurrence of flip, Neimark-Sacker, and Turing bifurcations are discussed. It is shown that the patterns obtained are results of Turing, flip, and Neimark-Sacker instabilities. Numerical simulations are performed to verify the theoretical analysis and to reveal complex and rich dynamics of the model, such as times series, maximal Lyapunov exponent, bifurcation diagrams, and phase portraits. Interesting patterns like spiral pattern, polygonal pattern, and the combinations of patterns of spiral waves and stripes are formed. The CML model’s results help to understand how a spatially extended, discrete intraguild predation model forms complex patterns. Notably, the continuous reaction–diffusion counterpart of the model under study is incapable of experiencing Turing instability.

We numerically investigate the deterministic dynamics of a one-dimensional particle in a symmetric periodic potential under the influence of an external periodic force. Additionally, we introduce asymmetry into the system by applying a space–time dependent frictional force. A simple physical example of the theoretical problem studied might be the propagation of a longitudinal sound wave in a symmetric periodic system. This leads to compression and rarefaction in the medium, resulting in particles being subjected to a damping force that periodically fluctuates in both space and time. Our objective is to investigate whether, during this process, net particle transport can be achieved within the considered inhomogeneous deterministic ratchet system and explore the necessary conditions for this to occur. We identify the various regimes of particle motion as manifested by the particle mean velocity as a function of the driving force amplitude. There are primarily three regimes: periodic intrawell, periodic interwell, and chaotic regimes observed. Ratchet effect is observed in both the periodic interwell and chaotic regimes; however, our focus lies on studying particle dynamics within the periodic interwell regime and exploring any relation between the constant ensemble-averaged current in that regime and the frequencies of the frictional force and applied external force. Furthermore, we demonstrate multiple dynamical attractors present under certain circumstances in the system analysed.

In this paper, we mainly investigate the geometric based relationship between the Katugampola fractional calculus and a Weierstrass-type function whose graph can be characterized as a fractal basin boundary for a random dynamical system. Using the potential-theoretic approach with some classical analytical tools, we have derived some kinds of fractal dimensions of the graph of the Katugampola fractional integral of this fractal function. It has been shown that there is a linear relationship between the order of the Katugampola fractional integral and the fractal dimension of the graph of this generalized Weierstrass function. Numerical results have also been provided to corroborate such linear connection.

The aim of this paper is to discuss the constructivity of the method originally introduced by U. Bessi to approach the phenomenon of topological instability commonly known as Arnold’s Diffusion. By adapting results and proofs from existing works and introducing additional tools where necessary, it is shown how, at least for a (well known) paradigmatic model, it is possible to obtain a rigorous proof on a suitable discrete space, which can be fully implemented on a computer. A selection of explicitly constructed diffusing trajectories for the system at hand is presented in the final section.

In this paper, we consider the coupled KdV equation

$\left(\begin{array}{cc}{\eta }_t+w_x+{\left(w\eta \right)}_x+\frac{1}{6}{w}_{xxx}& =0,\\ w_t+{\eta }_x+w{w}_x+\frac{1}{6}{\eta }_{xxx}& =0\end{array}\right)$

on $T=R/2\pi Z$ with initial data of small amplitudes $\varepsilon$ in Sobolev spaces. If the first three Fourier modes of initial data are of size ${\varepsilon }^{1+\mu }$ for any $0\le \mu \le \frac{1}{2}$, we prove that the solutions remain smaller than $2\varepsilon$ for a time scale of order ${\varepsilon }^{-(1+\mu )}$ via a normal form transformation. Further, we show this order of time scale is sharp.

We perform a stochastic model reduction of the Kuramoto–Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronised oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronised cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronised oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein–Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter.

We study the phase space of a particle moving in the gravitational field of a rotating black hole described by the Kerr metric from a geometrical perspective. In particular, we show the construction of a multidimensional generalization of the unstable periodic orbits, known as Normally Hyperbolic Invariant Manifolds, and their stable and unstable invariant manifolds that direct the dynamics in the phase space. Those stable and unstable invariant manifolds divide the phase space and are robust under perturbations. To visualize the multidimensional invariant sets under the flow in the phase space, we use a method based on the arclength of the trajectories in phase space known as Lagrangian descriptors in the literature.

In this study, the analytical, integrability, and dynamical properties of an epidemic COVID-19 model called SEIARM, a six-dimensional coupled nonlinear system of ordinary differential equations from the mathematical point of view, are investigated by the artificial Hamiltonian method based on Lie symmetry groups. By constraining some constraint relations for the model parameters using this method, Lie symmetries, first integrals, and analytical solutions of the model are studied. By examining key factors like how many people are susceptible, infected, or recovered, we unveil hidden patterns and “constraints” within the model. These “constraints” show us how the virus might spread under different conditions, especially when a crucial number called $\Psi$ is between 0 and 1, providing valuable insights into the potential spread of COVID-19 and the effectiveness of control measures. The analytical solutions and their graphical representations for some real values of model parameters obtained from China during the pandemic period are also provided.