This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is numerically integrated and the control parameter is switched periodically within a chosen set of parameter values. The resulted attractor matches with the attractor ...

The existence of a global attractor is proved for the skew-product semiflow induced by almost periodic Nicholson systems and new conditions are given unique positive solution which exponentially attracts every other solution. Besides, some numerical simulations included to illustrate our results in concrete systems.

The non-linear dynamics of a chaotic attractor offer a number of useful features to the developer of neuromorphic systems. Included in these is the ability for efficient memory storage and recall. A chaotic attractor has a potentially infinite number of Unstable Periodic Orbits (UPO) embedded within it. These orbits can be stabilised with the application of delayed feedback inhibition. This res...

When a dynamical system exhibits transient chaos and a nonchaotic attractor, as in a periodic window, noise can induce a chaotic attractor. In particular, when the noise amplitude exceeds a critical value, the largest Lyapunov exponent of the attractor of the system starts to increase from zero. While a scaling law for the variation of the Lyapunov exponent with noise was uncovered previously, ...

A phase-field system of coupled Allen–Cahn type PDEs describing grain growth is analyzed and simulated. In the periodic setting, we prove the existence and uniqueness of global weak solutions to the problem. Then we investigate the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. Namely, the problem possesses a global attractor as well...

Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of boundary crisis is associated with curves of homoor heteroclinic tangency bifurcations of saddle periodic orbits. It is known that the locus of boundary crisis contains many gaps, corresponding to channels (regions of positive measure) where a non-chaotic attra...

The joint activity of neural populations is high dimensional and complex. One strategy for reaching a tractable understanding of circuit function is to seek the simplest dynamical system that can account for the population activity. By imaging Aplysia's pedal ganglion during fictive locomotion, here we show that its population-wide activity arises from a low-dimensional spiral attractor. Evokin...

We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable φ, endowed with periodic boundary conditions. We analyze the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. We first prove...

The paper devotes to the slow–fast behaviors of a higher-dimensional non-smooth system with coupling two scales. Some novel bursting attractors and interesting phenomena are presented, especially so-called mixed-torus oscillations, in which trajectory moves along different tori turn, though attractor still behaves quasi-periodic form. Based on 4-D hyper-chaotic model scrolls, modified version i...

We consider discrete equivariant dynamical systems and obtain results about the structure of attractors for such systems. We show, for example, that the symmetry of an attractor cannot, in general, be an arbitrary subgroup of the group of symmetries. In addition, there are group-theoretic restrictions on the symmetry of connected components of a symmetric attractor. The symmetry of attractors h...