# Questions tagged [complex-systems]

This tag is for questions regarding to complex system, a system composed of many components which may interact with each other.

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### What are the latest advancements with regards to complex systems?

I am an endocrinologist, 90 years old, interested in finding out the latest developments in the field of complex systems. I am not aware if this concept is still valid in today's modern mathematical ...
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### Variation of graphs with respect to "number of nodes" vs fixed "number of nodes"

I am having a hard time finding mathematical discussion on variation of graphs with respect to number of "nodes". It seems graph theoretical/network analysis is very much focused on networks ...
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### Can you modeling complicated dynamics without using differential/difference equations?

Let's imagine there is a phenomenon I want to understand. I have a few multivariate time series about the phenomenon but not a lot. I don't know how the variables are related to each other but from ...
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### What's the relationship between these processes?

A snow ball rolling down a mountain: It's surface area gets bigger, thus the ball collects more snow until it can't hold it's own weight anymore. Two hot dog stands are next to each other: If one has ...
131 views

### How much algebra is preferable for studying/doing research in dynamical/complex system and networks

This question seems quite broad to ask... The situation here is that I'm a second-year undergrad student majoring in math and statistics. I'm really interested in fields like complex system and ...
1 vote
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### Hessian Matrix with infinite Eigenvalue

I'm dealing with an optimization problem, so I need to determine if I get maximum, minimum, or saddle points in a function of two variables. However, When evaluating the eigenvalues o my Hessian ...
1 vote
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### Is the set of all grammatically correct words a lattice and is there grammar for which this set is not lattice?

Let G be a formal grammar of any Chomsky type (as defined by the production rules) and let the production rules establish the order among words of this grammar: words a and b are a<=b if a can be ...
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### Strange fixed point in state space

I'm studying the following dynamical system, \begin{align} \dot{x} &= y \,\, , \\ \dot{y} &= \frac{\left(-4 x^3+33 x^2-78 x+54\right) y^2+(x-3) (2 x-6)^2}{(3-2 x) (2-x) x (2 x-6)} \,\, , \end{...
133 views

### Can synchronized chaotic systems be periodic or stochastic?

I am confused regarding the terms chaotic, periodic, and stochastic in the context of coupled chaotic systems: In general, if chaotic systems are coupled together and synchronized then does the ...
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### Conservation of the Hamiltonian

I'm struggling with the following calculus of variation problem. For an autonomous problem, it is often said that the Hamiltonian is constant along an extremal trajectory. However, the proofs of that ...
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### Lyapunov-Stability - global asymptotic stability

sadly I wasn't able to find a 'control systems' community, so I'm posting here. I'm working through the book of H. Khalil - Nonlinear Systems and I'm stuck at the following part: He states the ...
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### How do you obtain the fixed points and stability of a piecewise function?

Hi so I'm trying to work out how to find the fixed points of a piecewise function and do a stability analysis. One of the past exam papers in this complex systems course I'm doing has this question: ...
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### Do a complex system's attribute changes always exhibit depedance?

Say a complex system C has an attribute A. Can I assert that a change of A is always – to some degree – dependent upon A’s past? My reasoning is the following: Any attribute of C is influenced by C....
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