What we see appears stable, even though neuronal activity is full of irregular fluctuations. A team led by Dr Mehdi Borjkhani from ICTER has shown, using a minimal model of the primary visual cortex, that two natural feedback mechanisms can constrain chaos and reduce variability in neural activity by up to 93 percent. The results offer a possible explanation for how the brain can remain flexible while reliably processing visual information.
Every glance triggers a complex exchange of signals between millions of neurons. Some cells excite the network, others inhibit it, while additional signals arrive from the thalamus and neuromodulatory systems. This activity does not run with the regularity of a clock. Nevertheless, we can recognize a face, judge the direction of an approaching car, or read a sign even when conditions change rapidly.
This flexibility is one of the fundamental paradoxes of the brain. The visual system must remain variable enough to respond to new information, but it cannot become fully chaotic. If it did, even a minimal difference in initial neural activity could soon produce a completely different response. Reliable encoding of visual stimuli would no longer be possible.
The problem was investigated by a team comprising Dr Mehdi Borjkhani from the International Centre for Translational Eye Research (ICTER), part of the Institute of Physical Chemistry, Polish Academy of Sciences, Morteza A. Sharif from Urmia University of Technology, and Hadi Borjkhani from HTW Berlin. Their findings were presented in the article, Intrinsic chaos control in cortical circuits: A minimal E-I-M rate model for the primary visual cortex , published in the Journal of Computational Neuroscience .
"In this context, chaos does not mean ordinary noise or disorder. It is a deterministic form of dynamics in which a very small difference at the beginning can rapidly take the entire system in a different direction. For the brain, this is a potential source of flexibility, but also a risk to stable information processing," says Dr Mehdi Borjkhani, first author of the publication.
Three variables instead of billions of neurons
The researchers did not attempt to reproduce every neuron and connection in the cortex. They developed a model covering three interacting populations. The E variable represented excitatory neurons, particularly pyramidal cells, which account for approximately 80 per cent of cortical neurons. The I variable represented fast inhibitory interneurons, especially PV+ cells. The M variable corresponded to slower modulatory drive, combining influences from the thalamus and neuromodulatory systems.
The starting point was an exceptionally simple chaotic Lotka-Volterra system, originally known from mathematical descriptions of interacting populations. It consists of only seven terms and two basic parameters. The authors emphasize that they used it as a mathematical scaffold, rather than as a literal description of synapses or individual cells.
They introduced three features characteristic of the visual cortex into the model. The first was feedback through which increasing activity of excitatory neurons recruits inhibitory neurons. The second was homeostasis, or self-regulation, which keeps modulatory drive within a safe range. The third was an orientation-tuned visual stimulus, such as a vertical, horizontal, or oblique edge.
The researchers tested 225 different versions of the model by varying the strength of excitation, inhibition, and background input. In its original form, almost nine out of ten settings led to chaos. This meant that even nearly identical starting conditions quickly developed in completely different ways. A positive Lyapunov exponent of 0.069 - a mathematical measure of how strongly a system reacts to tiny changes - confirmed this behaviour.
When the researchers added feedback mechanisms found in the brain, the model became markedly more stable. Irregular activity gave way to a steady, repeating rhythm, while variability fell from 0.325 to 0.024 - a reduction of 93 per cent. This was not the result of one carefully selected setting. The model stabilized across most of the tested conditions and remained robust even when most parameter values were changed by 25 per cent.
The situation changed after biologically motivated feedback mechanisms were introduced. The chaotic attractor was replaced by a stable cycle, while the variance of excitatory activity at the analyzed operating point decreased from 0.325 to 0.024. This change represents a reduction of 93 percent. Stabilization occurred across most of the examined parameter range, rather than at only one precisely selected setting. The model also remained stable after most parameters were changed by 25 percent.
"The most interesting point is that we did not have to remove the model's capacity for chaotic activity. It was enough to introduce mechanisms that the real cortex uses every day: rapid inhibition and slower self-regulation. At the operating point we examined, these mechanisms reduced variability by 93 percent," explains Dr Borjkhani.
Does the model behave like the visual cortex?
Merely stabilizing mathematical chaos was not enough. The authors therefore investigated whether the model could reproduce phenomena observed in the primary visual cortex, which is known as V1.
The researchers then tested how 30 virtual neurons responded to lines shown at 10 different angles, ranging from 0 to 180 degrees in 20-degree steps. They wanted to see whether individual neurons responded more strongly to a particular direction. This is measured using the orientation selectivity index, or OSI: zero means no preference, while one means that a neuron responds exclusively to a single orientation.
The average score was 0.38 ± 0.09 in the chaotic version of the model and 0.31 ± 0.10 in the more regular one. Both values fall within the range of 0.1-0.9 observed in the primary visual cortex of macaques. Interestingly, moderately irregular activity did not make orientation recognition less precise. On the contrary, neurons in the model distinguished their preferred direction slightly more clearly from the others.
The researchers also examined how the activity of the entire simulated network would affect a single neuron. To do this, they used the classic Hodgkin-Huxley model, which reproduces the generation of nerve impulses. They then compared how regularly the neuron fired under different types of input.
With chaotic input, the intervals between impulses varied much more than they did with regular signals. The coefficient used to measure this irregularity reached 0.27, compared with 0.05 for sinusoidal input and only 0.005 for a constant signal. The result of 0.27 falls within the range of 0.1-0.3 measured in cortical neurons under laboratory conditions. However, it remains clearly below the range of 0.7-1.0 observed in the living brain. This suggests that chaos may be one source of irregular neuronal activity, but other factors also contribute to it in the real brain.
New definition of stable vision
The study suggests that stable vision is not a passive state. It may be the result of continuous control over a system operating close to the boundary of instability. This near-threshold state allows the brain to respond rapidly while ensuring that the same visual scene does not produce a completely different response every time.
The model may also help researchers design future experiments on disturbances in the balance between excitation and inhibition. The authors predict that weakening excitatory-to-inhibitory feedback or homeostatic processes should increase the variability of cortical activity. Such a mechanism may be relevant to understanding the irregular patterns of neural activity observed in conditions including epilepsy and schizophrenia. At this stage, however, it remains a hypothesis that must be tested in biological experiments.
The model also has important limitations. It does not account for the spatial organization of the cortex, its layers, or the full diversity of interneuron types. The Hodgkin-Huxley neuron was used as a general spike generator, rather than as a detailed model of a V1 pyramidal cell. The study therefore does not yet provide a diagnostic tool or treatment.
"We are not proposing a ready-made therapeutic approach. We are providing a simple map of relationships and specific predictions that can be tested experimentally. If they are confirmed in real neural circuits, it will become easier to understand when the brain's natural variability supports information processing and when it begins to threaten it," concludes Dr Mehdi Borjkhani.
The most important conclusion from the team's work reverses the usual question. Perhaps we should not focus exclusively on how the brain generates complex, nearly chaotic activity. Rather, it is equally important to ask how the brain keeps this activity under control every day. Our stable perception of the world may depend precisely on this constant interplay between flexibility and order.
Mehdi Borjkhani, Morteza A. Sharif, Hadi Borjkhani (2026). Intrinsic chaos control in cortical circuits: A minimal E-I-M rate model for primary visual cortex . Journal of Computational Neuroscience .
DOI: https://doi.org/10.1007/s10827-026-00938-5
Author: Scientific Editor Marcin Powęska
Journal of Computational Neuroscience
Experimental study
Animals
Intrinsic chaos control in cortical circuits: A minimal E-I-M rate model for primary visual cortex
22-Jun-2026