# Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

@article{DiazRuelas2016TangentMI, title={Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.}, author={Alvaro Diaz-Ruelas and Henrik Jeldtoft Jensen and Duccio Piovani and Alberto Robledo}, journal={Chaos}, year={2016}, volume={26 12}, pages={ 123105 } }

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal…

## 6 Citations

### Relating high dimensional stochastic complex systems to low-dimensional intermittency

- Computer ScienceThe European Physical Journal Special Topics
- 2017

We evaluate the implication and outlook of an unanticipated simplification in the macroscopic behavior of two high-dimensional sto-chastic models: the Replicator Model with Mutations and the Tangled…

### Relating high dimensional stochastic complex systems to low-dimensional intermittency

- Computer Science
- 2017

Here the implication and outlook of an unanticipated simplification in the macroscopic behavior of two high-dimensional sto-chastic models: the Replicator Model with Mutations and the Tangled Nature Model of evolutionary ecology are evaluated.

### Manifestations of the onset of chaos in condensed matter and complex systems

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An analytical framework of nonlinear mappings that reproduce rank distributions of large classes of data (including Zipf’s law) is described, and a common circumstance of drastic contraction of configuration space driven by the attractors of these mappings is pointed out.

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We offer a brief description of a set of interrelated research lines on the physics of complex systems developed under a unifying methodology grown out from nonlinear dynamics of low dimensionality.…

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### Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case

- Computer ScienceJournal of Mathematics
- 2022

This paper introduces a structure of a general stochastic dynamical system that can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix and proves this structure for the high-dimension case.

## 17 References

### Evolution and non-equilibrium physics: A study of the Tangled Nature Model

- Biology
- 2014

This study uses extensive computer simulations of the Tangled Nature Model of biological evolution to show that punctuated equilibria successively generated by the model's dynamics have increasing entropy and are separated by increasing entropic barriers.

### Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

A study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution that provides selection through a reproduction probability that contains quenched, random interspecies interactions and genetic variation through a low mutation rate.

### Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise

- Physics
- 1991

In this book the author explores the idea's of scaling, self-similarity, chaos.

### Emergence of effective low-dimensional dynamics in the macroscopic behaviour of coupled map lattices

- Mathematics
- 1992

Bifurcation of democratically coupled logistic maps in various space dimensions are studied beyond the accumulation point of the direct cascade of the individual maps. In dimensions d = 2 and 3, only…

### Time-dependent extinction rate and species abundance in a tangled-nature model of biological evolution.

- BiologyPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

We present a model of evolutionary ecology consisting of a web of interacting individuals, a tangle-nature model. The reproduction rate of individuals characterized by their genome depends on the…

### Fluctuations and correlations in an individual-based model of biological coevolution

- Physics
- 2004

The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically.

### Deterministic chaos: An introduction

- Physics
- 1984

Preface.Color Plates.1 Introduction.2 Experiments and Simple Models.2.1 Experimental Detection of Deterministic Chaos.2.2 The Periodically Kicked Rotator.3 Piecewise Linear Maps and Deterministic…

### Cultural evolution as a nonstationary stochastic process

- SociologyComplex.
- 2016

The model is patterned on an established model of biological evolution, the Tangled Nature Model, where a ‘tangle’ of interactions between agents determines their reproductive success, and can qualitatively reproduce the flurry of cultural activity which follows a disruptive innovation.

### Intermittent transition to turbulence in dissipative dynamical systems

- Physics
- 1980

We study some simple dissipative dynamical systems exhibiting a transition from a stable periodic behavior to a chaotic one. At that transition, the inverse coherence time grows continuously from…

### Genetic distance and species formation in evolving populations

- BiologyJournal of Molecular Evolution
- 2004

Comparing the behavior of the genetic distance between individuals in evolving populations for three stochastic models of evolving populations and the theory of disordered systems in physics is compared.