Mathematics Stack Exchange
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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.

A complex system is a system with components that interact with each other.

Such systems are sometimes modeled as a network of nodes representing components and links representing interactions.

Examples of complex systems are Earth's climate, organisms, brains, social and economic organizations such cities, ecosystems, biological cells, and ultimately the entire universe.

Complex systems are often difficult to model due to the properties of the interactions, which include nonlinearity, emergence, spontaneous order, adaptation, and feedback loops.

27 questions
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How do I perform this complex integration?

Evaluate the complex integration $(z^2 + 3z)$ wrt $z$ along the circle $|z| = 2$, from $(2,0)$ to $(0,2)$ in a counterclockwise direction. As far as I understand, this can be solved by taking $x = 2 \cos \theta$, $y = 2 \sin \theta$, and then…
Jasmine
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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{align} and when I plot the phase space I get the…
Herr Schrödinger
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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 conventions or in philosophical terms.
Raul GUTIERREZ GUTIERREZ
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Compute dynamical systems quantities (e.g. box-counting dimension, lyapunov exponent) for multiple recordings of same system

I have multiple recordings of the same biological system, which were obtained at different times they are therefore not forming one single timeseries. Is there a way to combined them to study the underlying dynamical systems? At the moment what I am…
Johncowk
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Smoothly varying dynamical equations

If I have a set of differential equations describing the system in a regime, of the form: $\ddot x= a(t) \dot x + by+cx \\ \dot y=d(t)\dot x+ey+f(t)$ Now this system behaves according to this: $\dot x=g(t) + h(t)x$ in a different regime. I am…
Kaguro
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Can this problem be treated in purely mathematical way other than the graphical way?

Problem Statement: I attempted all the parts. For part (a), $E_1 = P + R + S$, so $ \dot E_1 = \dot P + \dot R + \dot S$. Plugging these values and rearranging the terms would get the desired expression. From any 3D plotter, we can see that…
Abdul Muhaymin
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