## 7 Citations

### Unphysical source of dynamic order for the natural world

- Physics
- 2016

The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem,…

### Nonlinear complexification of periodic orbits in the generalized Landau scenario.

- Mathematics, PhysicsChaos
- 2022

We have found a way for penetrating the space of the dynamical systems toward systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which…

### Emergence and Electrophysiological Analogies in Jellium Models for Cortical Brain Matter

- BiologyComplex Syst.
- 2017

This paper adopts the point of view that a significant share of neurons in a being can be modeled by (in this approach complex-valued) dynamical systems based on a manageable number of phase-space dimensions, thus representing a macroscopic overall description of the totality of highly redundant neuronal processes.

### Nonlinear oscillatory mixing in the generalized Landau scenario.

- PhysicsPhysical review. E
- 2018

A set of phase-space portraits illustrating the extraordinary oscillatory possibilities of the dynamical systems through the so-called generalized Landau scenario is presented, and a mathematical theory covering the mode-mixing mechanisms is lacking.

### Slow stochastic switching by collective chaos of fast elements.

- PhysicsPhysical review letters
- 2013

Coupled dynamical systems with one slow element and many fast elements are analyzed and the adiabatic kinetic branch is introduced by averaging over the dynamics of the fast variables, introducing the ubiquity of the phenomena in the slow-fast dynamics.

### Chaos with a high-dimensional torus

- PhysicsPhysical Review Research
- 2020

Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of…

### Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits

- Physics, Mathematics
- 2021

R. Herrero, J. Farjas, F. Pi, G. Orriols ⁎ Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, 08222 Terrassa, Spain ramon.herrero@upc.edu † Departament de Física,…

## 122 References

### N-dimensional dynamical systems exploiting instabilities in full.

- PhysicsChaos
- 2000

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation…

### Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems.

- BiologyThe Behavioral and brain sciences
- 2001

A new coding scheme of information in chaos-driven contracting systems the authors refer to as Cantor coding is proposed, found in the hippocampal formation and also in the olfactory system, which should be of biological significance.

### Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time…

### Pattern formation outside of equilibrium

- Physics
- 1993

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples…

### Self-Organizing Systems

- PhysicsLife Science Monographs
- 1987

This chapter describes the efforts of cosmologists (and nature?) to form galactic and stellar structures, comments on them from the viewpoint of the homeokinetic principles, and pursues some parallels in the origin of life.

### The dynamics of coherent structures in the wall region of a turbulent boundary layer

- PhysicsJournal of Fluid Mechanics
- 1988

We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem…