Rulkov map

This saves memory and simplifies the computation of large neural networks.

does not have explicit biological meaning, though some analogy to gating variables can be drawn.

give rise to different dynamical states of the neuron like resting, tonic spiking and chaotic bursts.

evolves very slowly, for moderate amount of time it can be treated as a parameter with constant value in the

variable's evolution equation (which we now call as one dimensional fast submap because as compared to

One of these fixed points is stable, another is unstable and third may change the stability.

increases, two of these fixed points (stable one and unstable one) merge and disappear by saddle-node bifurcation.

Coupling of two neurons has been investigated by Irina Bashkirtseva and Alexander Pisarchik who explored transitions between stationary, periodic, quasiperiodic, and chaotic regimes.

[4] They also addresses the additional consequences of random disturbances on this system, leading to noise-induced transitions between periodic and chaotic stochastic oscillations.

[5] Adaptations of the Rulkov map have found applications in labor and industrial economics, particularly in the realm of corporate dynamics.

[6] The proposed framework leverages synchronization and chaos regularization to account for dynamic transitions among multiple equilibria, incorporate skewness and idiosyncratic elements, and unveil the influence of effort on corporate profitability.

The results are substantiated through empirical validation with real-world data.

[6] Orlando and Bufalo introduced a deterministic model based on the Rulkov map,[7] effectively modeling volatility fluctuations in corporate yields and spreads, even during distressed periods like COVID-19.

Nevertheless, the deterministic nature of the Rulkov map model may provide enhanced explanatory capabilities.

[8] Other applications of the Rulkov map include memristors,[9][10] financial markets,[11][12] biological systems,[13] etc.