dynode 0.1.0.dev0

A framework for modelling and simulation of dynamical systems

dynode

A framework for modelling and simulation of dynamical systems in the form of ordinary differential equations.

Requires python >= 3.6

Dynode solves equations of the form y' = f(t, y) using SciPy's ode solver but allows f to be modelled in a modular, object-oriented fashion using the notions of separate Systems that expose states and their corresponding derivatives, ders. f may then be composed of an arbitraily complex collection of, connected or unconnected, Systems.

Example: Single Van der Pol oscillator

A well-known dynamical system is the Van der Pol oscillator, which is described by a second-order differential equation:

Rewriting it to a system of ordinary differential equations yields:

In dynode, a Van der Pol system may be modelled as:

from dynode import SystemInterface

class VanDerPol(SystemInterface):

    def __init__(self):
        super().__init__()

        self.inputs.mu = 1.0

        self.states.x = 0.0
        self.ders.dx = 0.0

        self.states.y = 0.0
        self.ders.dy = 0.0

    def do_step(self, time):
        mu = self.inputs.mu
        x = self.states.x
        y = self.states.y

        self.ders.dx = y
        self.ders.dy = mu*(1-x**2)*y - x

And may be simulated like this:

from dynode.simulation import Simulation

sys = VanDerPol()
sys.add_store('states', 'x')
sys.add_store('states', 'y')

sim = Simulation()
sim.add_system(sys)

sys.states.x = 1
sim.simulate(100, 0.1)

import matplotlib.pyplot as plt
plt.plot(sys.res.time, sys.res.x)
plt.plot(sys.res.time, sys.res.y)
plt.show()

Connected systems

Dynode systems accepts connections as callbacks registered to a system. The callback signature looks like:

def connection_callback(system, time):
    pass

where system is a reference to the system this callback is registered to and time is the current time in the simulation.

Connections can be either pre_step_connections or post_step_connections depending on if the callback should be called prior to or after the do_step-method of the system

Example: Two connected Van der Pol oscillators

Imagine the situation where you have two oscillators interacting as follows:

• The damping paramater (mu) of oscillator 1 is forced by a sinus wave according to 0.1*sin(0.1*t)
• The damping parmeter (mu) of oscillator 2 is forced to follow the the state y of oscillator 1

In dynode, the above scenario can be described and simulated as:

from dynode import connect_signals

sys1 = VanDerPol()
sys1.states.x = 1

sys2 = VanDerPol()

# Connecting state y of sys1 to input mu of sys2
sys1.add_post_connection(connect_signals(sys1.states, 'y', sys2.inputs, 'mu'))

# Forcing input mu of sys1 to follow a sinus function
def sinus_forcer(sys, t):
    sys.inputs.mu = 0.1*np.sin(0.1*t)

sys1.add_pre_connection(sinus_forcer)

sim = Sim()
sim.add_system(sys1)
sim.add_system(sys2)

sim.simulate(100, 0.1)