Dynamical neuroscience

The dynamical systems approach to neuroscience is a special way to study how living things think and feel using math. It looks at how tiny parts of our bodies, like cells in the brain, work together.

Dynamical neuroscience helps us understand how the brain works at many levels, from single cells to big thoughts and actions. It shows how the brain can switch between different states, like waking up or sleeping.

Neurons have been studied for many years, and dynamical systems can also appear in other parts of the nervous system. For example, chemicals in the brain can behave in surprising ways, and the flow of fluids around neurons also matters. By using ideas from information theory and thermodynamics, scientists can learn more about how the brain works.

History

Scientists first studied how neurons work using math and physics. In 1907, they made a simple model called the integrate-and-fire model. In 1952, two scientists named Alan Hodgkin and Andrew Huxley used a special part of a squid to create an even better model, called the Hodgkin–Huxley model. Other scientists made simpler versions of these models later.

As computers became more powerful in the late 20th century, they helped scientists study neurons in new ways. Computers could solve very hard math problems that were too difficult by hand. This led to the creation of a field called computational neuroscience. In 2007, a book called Dynamical Systems in Neuroscience by Eugene Izhikivech helped many people learn about this interesting area of study.

Neuron dynamics

Main article: biological neuron model

Neurons are special cells that help our brains send messages. Scientists study how neurons work using math and physics. They look at how the neuron's energy changes and how tiny doors in the neuron open and close.

When a neuron gets enough energy, special doors open to let tiny particles in or out. This changes the neuron's energy over and over, like a circle. This helps scientists understand how neurons talk to each other.

One famous example is called the Morris–Lecar model. It uses two main things: the neuron's energy (V) and a helper number (N) that tells how likely a door is open. These two things change over time based on each other. This helps scientists see how neurons can fire or send signals.

Neurons can act like balls in a lake. Normally, they stay still. But if something pushes them hard enough, they "fire" and send a message, then go back to rest. This is called excitability and helps neurons share information. Sometimes, neurons can also act like heart cells that keep beating on their own.

Global neurodynamics

The way groups of neurons work together depends on a few important things: how each neuron behaves, how they connect to each other, the layout of these connections, and outside influences like temperature changes.

We can create models of these networks by choosing how each neuron acts and how they interact. These models help us understand complex behaviors in the brain, like remembering things or recognizing smells. Some networks can show steady patterns, while others can change in more unpredictable ways.

Beyond neurons

Neurons are very important for how our brain works. But scientists now know that neurons depend on what’s around them. Right outside neurons, there is a special space with other cells called glial cells. These cells help neurons work.

Neurons also need many tiny chemical reactions to work. Inside each neuron, small parts called organelles use chemicals like G-proteins and neurotransmitters. They need energy from ATP. These chemicals help neurons send signals and stay active. This shows how complex our brain is.

Cognitive neuroscience

The computational approaches to theoretical neuroscience use artificial neural networks to study how the brain works. These networks simplify individual neurons to see how groups of neurons act together. Even though neural networks are often linked to artificial intelligence, they help us learn how the mind handles information.

Hopfield networks are a special type of neural network. They use a mathematical tool called the Lyapunov function to study stability in systems. These networks are important for learning how memories work, especially how hints can bring back memories. Stability in living systems is known as homeostasis.