Ctrl+K

JointEq

Contents

JointEq#

class brainpy.JointEq(*eqs)[source]#

Make a joint equation from multiple derivation functions.

For example, we have an Izhikevich neuron model,

>>> a, b = 0.02, 0.20
>>> dV = lambda V, t, u, Iext: 0.04 * V * V + 5 * V + 140 - u + Iext
>>> du = lambda u, t, V: a * (b * V - u)

If we make numerical solver for each derivative function, they will be solved independently.

>>> import brainpy as bp
>>> bp.odeint(dV, method='rk2', show_code=True)
def brainpy_itg_of_ode0(V, t, u, Iext, dt=0.1):
  dV_k1 = f(V, t, u, Iext)
  k2_V_arg = V + dt * dV_k1 * 0.6666666666666666
  k2_t_arg = t + dt * 0.6666666666666666
  dV_k2 = f(k2_V_arg, k2_t_arg, u, Iext)
  V_new = V + dV_k1 * dt * 0.25 + dV_k2 * dt * 0.75
  return V_new

As you see in the output code, “dV_k2” is evaluated by \(f(V_{k2}, u)\). If you want to solve the above coupled equation jointly, i.e., evalute “dV_k2” with \(f(V_{k2}, u_{k2})\), you can use brainpy.JointEq to emerge the above two derivative equations into a joint equation, so that they will be numerically solved together. Let’s see the difference:

>>> eq = bp.JointEq(eqs=(dV, du))
>>> bp.odeint(eq, method='rk2', show_code=True)
def brainpy_itg_of_ode0_joint_eq(V, u, t, Iext, dt=0.1):
  dV_k1, du_k1 = f(V, u, t, Iext)
  k2_V_arg = V + dt * dV_k1 * 0.6666666666666666
  k2_u_arg = u + dt * du_k1 * 0.6666666666666666
  k2_t_arg = t + dt * 0.6666666666666666
  dV_k2, du_k2 = f(k2_V_arg, k2_u_arg, k2_t_arg, Iext)
  V_new = V + dV_k1 * dt * 0.25 + dV_k2 * dt * 0.75
  u_new = u + du_k1 * dt * 0.25 + du_k2 * dt * 0.75
  return V_new, u_new

brainpy.JointEq supports make nested JointEq, which means the instance of JointEq can be an element to compose a new JointEq.

>>> dw = lambda w, t, V: a * (b * V - w)
>>> eq2 = bp.JointEq(eqs=(eq, dw))
Parameters:

*eqs – The elements of derivative function to compose.

Contents