# Read PDF Dynamics and Randomness (Nonlinear Phenomena and Complex Systems)

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The world is a bit more complex than this and behind this complexity is the fact that the dynamics of a system may be the product of multiple different interacting forces, have multiple attractor states and be able to change between different attractors over time. A classical example given of this is a double pendulum.

Nonlinear Dynamics: Introduction to Nonlinear Dynamics

A simple pendulum without a joint will follow the periodic and deterministic motion characteristic of linear systems with a single equilibrium. To take a second example, the dynamics of a planet orbiting another is an example of a linear system with a single equilibrium and attractor, but when we add another planet into this equation, we now have two equilibrium points creating a nonlinear dynamic system as our planet would be under the influence of two different gravitational fields of attraction.

## Complex Systems

Whereas with simple periodic motion it was not important where the system started out, there was only one basin of attraction and it would simply gravitate towards this equilibrium point and then continue in a periodic fashion. But when we have multiple interacting parts and basins of attraction, small changes in the initial state to the system can lead to very different long-term trajectories and this is what is called chaos.

Small differences in initial conditions yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. We should note that chaos theory really deals with deterministic systems, and moreover it is primarily focused on simple systems in that it often deals with systems that have only a very few elements, as opposed to complex systems where we have very many components that are nondeterministic.

In these complex systems, we would, of course, expect all sorts of random, complex and chaotic behavior, but it is not something we would expect in simple deterministic systems. This chaotic and unpredictable behavior happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.

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In other words, the deterministic nature of these systems does not make them predictable, which is deeply counter-intuitive to us. A double pendulum essentially consists of only two interacting components — that is each limb — and these limbs are both strictly deterministic when taken in isolation. But when we join them, this very simple system can and does exhibit nonlinear and chaotic behavior. The aim of the journal is to stimulate more research interest for exploration of discontinuity, complexity, nonlinearity and chaos in complex systems.

## Nonlinear Dynamics & Chaos

The manuscripts in dynamical systems with nonlinearity and chaos are solicited, which includes mathematical theories and methods, physical principles and laws, and computational techniques. The journal provides a place to researchers for the rapid exchange of ideas and techniques in discontinuity, complexity, nonlinearity and chaos in physical and social sciences. No length limitations for contributions are set, but only concisely written manuscripts are published. Brief papers are published on the basis of Technical Notes.