We review our recent work on ellipsoidal M2-brane solutions in the large-N limit of BMN matrix model. These bosonic finite-energy membranes live inside SO(3)xSO(6) symmetric plane-wave spacetimes and correspond to local extrema energy functional. They are static SO(3) stationary SO(6). Chaos appears at level radial stability analysis through explicitly derived spectrum eigenvalues. The angular ...

We analyze a continuous gene expression model on the underlying topology of a complex heterogeneous network. Numerical simulations aimed at studying the chaotic and periodic dynamics of the model are performed. The results clearly indicate that there is a region in which the dynamical and structural complexity of the system avoid chaotic attractors. However, contrary to what has been reported f...

A class of RC-OTA hysteretic-chaotic oscillators has been previously reported using electronics; therefore, hysteresis is realized by an electronic circuit. To obtain a mathematical model of this RC-OTA chaotic-electronic device, hysteresis modeling turns an important issue. Here, we develop a new mathematical hysteretic model proposing a new jounce-chaotic oscillator. Chaosity test is proved u...

Title of dissertation: STATISTICAL MODELING OF WAVE CHAOTIC TRANSPORT AND TUNNELING Ming-Jer Lee, Doctor of Philosophy, 2013 Dissertation directed by: Professor Edward Ott Professor Thomas Antonsen Department of Physics This thesis treats two general problem areas in the field of wave chaos. The first problem area that we address concerns short wavelength tunneling from a classically confined r...

A class of RC-OTA hysteretic-chaotic generators has been proposed from the electronics point of view. Hysteresis is captured by an electronic realization. To extend its applicability, hysteretic mathematical modeling is an important issue. Here, a new hysteretic model is proposed. With this model, we realized a well known hysteretic-chaotic attractor using Simnon.

We introduce an exceptionally simple gated recurrent neural network (RNN) that achieves performance comparable to well-known gated architectures, such as LSTMs and GRUs, on the word-level language modeling task. We prove that our model has simple, predicable and non-chaotic dynamics. This stands in stark contrast to more standard gated architectures, whose underlying dynamical systems exhibit c...

Chaotic dynamical systems are present in the nature in various forms such as the weather, activities in human brain, variation in stock market, flows and turbulence. In order to get a detailed understanding of a system, the modeling and analysis of the system is to be done in an effective way. A recurrent neural network (RNN) structure has been designed for modeling the dynamical system. The ne...