Marine ecosystems are increasingly recognized as exhibiting the principal hallmarks of complex systems, including the possibility of sudden shifts in state among alternative basins of attraction and both periodic and aperiodic dynamical behavior. Over the last several decades a well-defined theory of complexity has emerged, integrating earlier (and inter-related) concepts based on bifurcation t...

We demonstrate that sparse regression and compressive sensing techniques are capable of accurately determining a set of functions governing a nonlinear dynamical system. We analyze a technique introduced by Brunton, Proctor, and Kutz, 2016 [1] that builds a sparse representation of a dynamical system by computing sequential least squares fittings of the data to identify the governing equations....

modeling and analysis of future prices has been hot topic for economic analysts in recent years. traditionally, the complex movements in the prices are usually taken as random or stochastic process. however, they may be produced by a deterministic nonlinear process. accuracy and efficiency of economic models in the short period forecasting is strategic and crucial for business world. nonlinear ...

Nonlinear vibration of parabolic springs employed in suspension system of a freight car has been studied in this paper. First, dynamical behavior of the springs is investigated by using finite element method and the obtained results are then used in vibration analysis of a railway freight car. For this purpose, dynamics of a parabolic spring subjected to a cyclic excitation has been studied ...

Abstract: A mathematical model of architecture and learning processes of multilayer artificial neural netwoks is discussed in the paper. Dynamical systems theory is used to describe the learning precess of networks consisting of linear, weakly nonlinear and nonlinear neurons. Conjugacy between a gradient dynamical system with a constant time step and a cascade generated by its Euler method theo...

A fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model. Also different from other models, a model with the order 2 α is discussed. We are expecting an acceleration in feelings; that is why we increase the order of the derivative between 1 < 2α ≤ 2. Stability analysis of the fractional-order nonlinear...

The non-isothermal continuous stirred tank reactor (CSTR) is a classical yet complex case study of nonlinear dynamical systems. Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system and it rests on the formulation of the dynamics in the Brayton-Moser form. The Brayton-Moser formulation of the non-isothermal continuous stirre...

Phase structure of nonlinear dynamical system is governed by the vector field and decides the trajectories. Accordingly, the power spectra of trajectories include the structural field effect on the phase space. In this paper, we develop a method for analyzing phase structure using power spectra of trajectories and reconstitute a potential function in the system. key words: power spectra, potent...

In this paper, a specific neural-based model for identification of dynamical nonlinear systems is proposed. This artificial neural network, called State-Space Neural Network (SSNN), is different from other existing neural networks. Indeed, it uses a state-space representation while being able to adapt and learn its parameters. These parameters are the neural weights which are intelligible or un...

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of ...