Theta model

The theta model, or Ermentrout–Kopell <a href="/facts/Canonical_form/K2jhB44k">canonical</a> model, is a <a href="/facts/Biological_neuron_model/eCPeWaXc">biological neuron model</a> originally developed to mathematically describe neurons in the animal <a href="/facts/Aplysia/NzU0uLKI">Aplysia</a>. The model is particularly well-suited to describe neural <a href="/facts/Bursting/6u4F6c9M">bursting</a>, which is characterized by periodic transitions between rapid oscillations in the <a href="/facts/Membrane_potential/DpNG14c7">membrane potential</a> followed by quiescence. This bursting behavior is often found in <a href="/facts/Neurons/G7CyTVdH">neurons</a> responsible for controlling and maintaining steady rhythms such as breathing, swimming, and digesting. Of the three main classes of bursting <a href="/facts/Neurons/G7CyTVdH">neurons</a> (<a href="/facts/Bursting/6u4F6c9M">square wave bursting</a>, <a href="/facts/Parabolic_bursting/gp9fK5GE">parabolic bursting</a>, and elliptic bursting), the theta model describes <a href="/facts/Parabolic_bursting/gp9fK5GE">parabolic bursting</a>, which is characterized by a parabolic frequency curve during each burst.
The model consists of one <a href="/facts/State_variable/HNF1dCXu">variable</a> that describes the membrane potential of a neuron along with an input current. The single variable of the theta model obeys relatively simple <a href="/facts/Ordinary_differential_equation/ygKGQ8kD">equations</a>, allowing for <a href="/facts/Analytical_expression/y0xCXlSk">analytic</a>, or <a href="/facts/Closed-form_expression/y0xCXlSk">closed-form</a> solutions, which are useful for understanding the properties of parabolic bursting neurons. In contrast, other biophysically accurate neural models such as the <a href="/facts/Hodgkin%E2%80%93Huxley_model/HMuK0gP9">Hodgkin–Huxley model</a> and <a href="/facts/Morris%E2%80%93Lecar_model/MBA6n6vB">Morris–Lecar model</a> consist of multiple variables that cannot be solved analytically, requiring <a href="/facts/Numerical_methods_for_ordinary_differential_equations/rbrYBco3">numerical integration</a> to solve.
Similar models include the <a href="/facts/Quadratic_integrate_and_fire/qXxBbruA">quadratic integrate and fire</a> (QIF) model, which differs from the theta model only by a <a href="/facts/Change_of_variables/vjWdXCDF">change of variables</a> and Plant's model, which consists of Hodgkin–Huxley type equations and also differs from the theta model by a series of coordinate transformations.
Despite its simplicity, the theta model offers enough complexity in its <a href="/facts/Dynamical_system/782gREl5">dynamics</a> that it has been used for a wide range of <a href="/facts/Theoretical_neuroscience/eclSYyJK">theoretical neuroscience</a> research as well as in research beyond <a href="/facts/Biology/1M1ee3pB">biology</a>, such as in <a href="/facts/Artificial_intelligence/lJGauQwX">artificial intelligence</a>.

Theta model open-in-new

Theta model