Global Dynamics Processes: the Pattern which Connects from KaliYuga to Tao

A possible cataloging , not exhaustive, of the various types of systems based on the structure, function, internal properties or of input/output can be:

Absurd-Meaningless - Impossible, by constrast: Ingenious

These are systems for which the selection and composition of elements and/or the types of relationships/connections that are chosen do not have any sense or are inconsistent with fundamental laws.
It's worth noting that many fundamental discoveries were born to find meaning or links in natural or conceptual systems, where before it was thought there were not.

Trivial

These are systems whose description/analysis/knowledge does not add any information.

Simple

These are systems whose structure/functionality is easy to analyze/describe/implement.

Elementary

These are systems that have basic features but whose structure/description is not necessarily simple.

Deterministic / Random-Stochastic

This terms generally refer to the internal state of the system (defined by the set of internal state observable variables or to the characteristic of input/output. If a defined state of the system is a precise and unique state of the process or if a set value input produces always a defined output value then the system is deterministic - once determined these values are valid forever. If the values are descrivable by a probabilistic random variable the system is random, also known as dynamic random or stochastic, governed by a certain probability distribution on the values. Typically this means that some parts of the system/subsystem/processes are of random/probabilistic nature.

with/ without Memory

In systems with memory the system status and/or the value of the input/output function depend on the state or the input of the past.

linear / nonlinear

This term refers to the in/out function of the system, whether linear or not.
Typically a system is only linear in the range of values over a certain dynamic of values, the input / output becomes non-linear, such as saturation. A typical example of linear system are the amplifiers.

Linear systems are the only ones that can have a complete formal description of their features. A technique for dealing with nonlinear systems is to linearize them for a certain range of values, or simulate them by one or more linear systems.

stationary / non stationary

Systems are stationary (or time invariant) when the internal parameters do not depend on time but are constant.

static / dynamical

Among all the linear systems are of particular interest those lwhich are linear and stationary, for which the output signal depends only on the instantaneous value of the input signal. Conversely, there are linear dynamic systems, which are those systems for which the response depends - as well as input from the actual value - even from its past history.

open / closed / isolated / adiabatic

Open systems, first defined by von Bertalanffy, are systems that can thermodynamically interact with the external environment exchanging both energy (work or heat) and matter.

A closed system is a system that does not exchange mass with the external environment, while it may carry exchange of energy in all its forms (including heat) or work.An isolated system is a system that does not interact in any way with the environment, or which does not exchange neither mass, nor work and heat.

An adiabatic sistem is a closed system that can not exchange heat or matter with the external environment, but can exchange work.

concentrated / distributed constants

It is a terminology normally applied to systems circuit. If the minimum wavelength of the signals passing through a circuit is large compared to the components/elements of the circuit is said to be with constant-concentrated, conversely if it is comparable is called with distributed parameters. A typical example are microwave circuits, where the wavelength of the signals is the order of cm. or mm.

discrete time /continuous time

It is an alternative and more genera definition for the values/variables/processes of digital/analog types. If the variables or processes of the system are discrete in time, or only may take certain discrete values, the system is discrete-time, while if they have continuous values over time are continuous time.

discrete states-events / continuous states-events

Similar to the precedent for the system internal states.

synchronous / asynchronous / syncronicity

In the first two types we refer in general to the comparison between the internal processes of the system or of some internal processes and other external to the system boundary. If the two processes have a correlation, usually in time, of the one-to-one among them, such as the type of cause and effect, these processes are synchronized with each other, while if they are temporally independent are called asynchronous.

The term syncronicity was introduced by Carl G. Jung in 1950 to describe a connection between events, psychological or objective, which occur synchronously, ie at the same time, but between which there is not a relation of cause and effect but a clear commonality of meaning. By extension, a system is synchronic when has relations between internal and/or external processes of synchronic type.

Paradoxical or Oscillators

The oscillatory systems are those where the internal states, processes or the system's output are of oscillation type , with a period, usually in time. The oscillation of the state or output can be generated by a system internal or internal/external paradox , for example of the type "if not then yes - if yes then not"; in this case the state or the system output becomes a continuous oscillation of yes and no.

Strange Loop

The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter to describe a situation where by moving up or down through a hierarchical system one finds oneself back where one started. Strange loops may involve self-reference and paradox. By extension strange loop systems are those where internal processes are of this type.

Chaotic

A dynamical sistem is of chaotic type if it has the following three main characteristics:

Sensitivity to initial conditions, that is to infinitesimal variations of the boundary conditions (or, generally, of the inputs) match with finite variations in the output. As a trivial example: the smoke of burning matches under the most very similar conditions (pressure, temperature, air currents) follows trajectories from time to time very different.
Unpredictability, ie it is not possible to predict in advance the performance of the system on long times compared to the characteristic time of the system starting from assigned boundary conditions.
The evolution the system is described, in the phase space, by many stochastic trajectories as seen by an external observer, which all remain confined within a defined space: the system that is not evolving toward infinity, for any variable; in this case we speak of 'attractors' or even 'deterministic-chaos'.

A chaotic system is deterministic in general, that is regulated by a very precise law that requires to assume a certain state (given its previous history and the law). The special feature of chaotic systems (a result of which are often confused with the random systems) is the fact that the upgrading law strongly depends on the initial conditions: a tiny change in initial conditions lead the system in a state far from what it could have achieved without this small variation.

Fractals

The term fractal was coined in 1975 by Benoît Mandelbrot, and derives from the Latin fractus fraction; in fact fractal images are considered by the mathematical objects with fractionary dimension. A fractal is a geometric object that is repeated in its structure the same on different scale, or that its aspect does not change at any magnification. This feature is often called self-similarity. The distinctive feature of fractals is that while the generation rules are relatively simple, their result produces meta-infinites.
By extension, fractal systems are those where processes or even the elements are of a fractal type.

Synergistic

The term synergetics was introduced by Hermann Haken within theframe of laser physics in the 70-80 years .Is commonly defined as a combined action of two or more elements, resulting in enhanced efficacy compared to their simple summation. It follows that a synergy is a simultaneous action of two phenomena, forces, or other entity, which strengthens the individual effects. A system is synergistic if one of its internal or external/internal processes have a synergy.

refer to: (Center for Synergetics, Stuttgart University)

Undecidable

It is a characteristic that occurs in a particular set of dynamic systems called finite automata, in particular for the Turing machine (TM). A TM (similar in all effects to a computer) is a formal system which can be described as an ideal mechanism, but in principle feasible, which can be in well-defined states (state machine), operating on strings according to strict rules and is a computing model. In a system of this type one pose the halting problem, or if it always possible in a TM, which has unlimited evolution, described a program and a given finite input, decide whether this program will end or will recur indefinitely. It was shown that there can be no general algorithm that can solve this problem for all possible inputs.

Complicated/Complex

The term complicated derives from complicatus, ie "with folds", and can be explained by the socalled classic science, while complex (from complexus, ovvero "weaving") cannot be explained by classical science.

The definition of complexity is itself complex - many authors in different fields have proposed their own definition of complexity. Moreover, the distinction between complicated and complex is not clear, both systems have in general the following features:

structure with many elements already in themselves complex
non-linear interactions among the elements
open system type
structure very often of net-type
necessity for the description of hierarchical and/or logical levels

Generally the characteristics of a complex system are that its elements are undergoing continuous changes individually predictable, but which is not possible or is very difficult to predict a future state.Moreover, complex systems can present a emergence behaviour, or a situation in which a system exhibits inexplicable properties on the basis of the laws governing its components. This fact arises from non-linear interactions among the system's comoponenets. Furthermore the system has adaptive characteristics, or modifies its parameters, elements and processes according to different inside or outside situations.
In general all living systems are complex while artificial systems can be very complicated but not necessarily complex, or with a degree of complexity much lower than the living ones.

The best example of a complicated system is Internet, a set of transmission networks based on the same protocol, which at present interconnects some hundreds of millions of machines among clients, hosts, servers and networks equipments such as switchs and routers. Though Internet, as well as being very complicated, has indeed a certain degree of complexity - due to its network structure, the number of elements, the interactions between them and the hierarchy levels of the communication protocol used (IP) - still has a complexity much less than the smallest living organisms, such as those unicellular like protozoa, or single cells.

Other examples of complex systems are cellular automaton, the earth's crust, considered as a dynamic system in the plate tectonics, all the ecosystems (even the simplest), the economical systems, the social systems, the nervous system , the climate systems, local or global.

Hologramatic

by extension of the physical case, obtained with laser interference, they are complex systems in which any partial subset arbitrarily divided contains the structure of the entire system.

The description of systems with feedback developed by cybernetics in the 40s and 50s is not enough when one considers systems that have different logical levels of description such , in general, complex systems, which contain many feedbacked subsystems and have several retroactive stabilization processes at many, such, for example, as metabolism:

The notion of complexity also marks the transition from first to second cybernetics: according to the first cybernetics an objective and external reality exists independent of the observer. In the system approaches according to the second-cybernetic the system, that is the set of elements that are interacting in the observable reality, it is comprehensive, dynamic and consists of two subsystems individual/environment in which the role of the observing subject is fundamental and should be taken into account in describing the global system. In complex systems, such as an animal, person, family or organization, we observe the system under observation and describe it exactly as the system observes and describes us.

Each of the two subsystems evolve according to its own logic and implement their own changes, but it is the other subsystem that determines the conditions that define the transformation that each subsystem implements.

In the second cybernetics subject and object, knower and the known are part of the same system. The individual and the environment are no longer places of property whose identification and description is under the responsibility of the outside observer, but location of mechanisms governed by their own rules, which determine the footage of their reciprocal interactions. The reality, no longer independent of the observer that actively builds it, becomes the personal reality of each individual, and any personal vision of reality comes from a specific relationship between knower and known, which reflects self-specific constraints. The individual thus becomes a cognitive system with its own internal coherence that can filter the reality, and structured through a set of constructs and beliefs that allow them to organize their behavior in response to the environment, according to its own self-constraints. The second cybernetics, seen as meta-cybernetics of the first cybernetics or simple, cybernetics, is characterized by subsequent orders of feedback:

and from the recursion between the orders of feedback and those of calibration which follow the feedback process:

taken from:

A simple feedback brings the system to calibrate itself to stability. A feedback of feedback leads him into a state of meta-calibration. A further level of feedback brings the system in what is called a stand-alone system, where the relationships and interactions that define it as a whole are determined only by the system itself, or autopoietic system, with a meta-meta-meta-calibration of closed organization.