{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c95b48fe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T08:13:01.777170Z",
     "iopub.status.busy": "2026-06-19T08:13:01.776937Z",
     "iopub.status.idle": "2026-06-19T08:13:07.108522Z",
     "shell.execute_reply": "2026-06-19T08:13:07.107867Z"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import brainmass\n",
    "import brainstate\n",
    "import brainunit as u\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "brainstate.random.seed(0)\n",
    "brainstate.environ.set(dt=0.1 * u.ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f918a67",
   "metadata": {},
   "source": [
    "# Larter-Breakspear Model\n",
    "\n",
    "The **Larter-Breakspear model** is a conductance-based mean-field model derived from the Morris-Lecar equations, with mean membrane potential $V$, a potassium gating variable $W$, and an inhibitory variable $Z$. Voltage-gated Na$^+$, K$^+$ and Ca$^{2+}$ currents make it capable of fixed points, limit cycles, and chaos depending on parameters. The pyramidal firing-threshold variance $d_V$ is a particularly effective knob for selecting the dynamical regime.\n",
    "\n",
    "**Reference:** Breakspear, Terry & Friston (2003), *Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics*, Network: Computation in Neural Systems 14(4):703-732."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73f7e423",
   "metadata": {},
   "source": [
    "## Build the model\n",
    "\n",
    "We pick `d_V = 0.57`, which puts the node in a limit-cycle band."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91191e33",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T08:13:07.110969Z",
     "iopub.status.busy": "2026-06-19T08:13:07.110550Z",
     "iopub.status.idle": "2026-06-19T08:13:07.137898Z",
     "shell.execute_reply": "2026-06-19T08:13:07.136454Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LarterBreakspearStep(\n",
       "  in_size=(1,),\n",
       "  out_size=(1,),\n",
       "  gCa=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1.1, dtype=float32)\n",
       "  ),\n",
       "  gK=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(2., dtype=float32)\n",
       "  ),\n",
       "  gL=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.5, dtype=float32)\n",
       "  ),\n",
       "  gNa=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(6.7, dtype=float32)\n",
       "  ),\n",
       "  TCa=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(-0.01, dtype=float32)\n",
       "  ),\n",
       "  TK=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0., dtype=float32)\n",
       "  ),\n",
       "  TNa=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.3, dtype=float32)\n",
       "  ),\n",
       "  d_Ca=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.15, dtype=float32)\n",
       "  ),\n",
       "  d_K=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.3, dtype=float32)\n",
       "  ),\n",
       "  d_Na=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.15, dtype=float32)\n",
       "  ),\n",
       "  VCa=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  ),\n",
       "  VK=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(-0.7, dtype=float32)\n",
       "  ),\n",
       "  VL=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(-0.5, dtype=float32)\n",
       "  ),\n",
       "  VNa=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.53, dtype=float32)\n",
       "  ),\n",
       "  phi=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.7, dtype=float32)\n",
       "  ),\n",
       "  tau_K=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  ),\n",
       "  aee=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.4, dtype=float32)\n",
       "  ),\n",
       "  aei=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(2., dtype=float32)\n",
       "  ),\n",
       "  aie=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(2., dtype=float32)\n",
       "  ),\n",
       "  ane=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  ),\n",
       "  ani=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.4, dtype=float32)\n",
       "  ),\n",
       "  b=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.1, dtype=float32)\n",
       "  ),\n",
       "  C=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.1, dtype=float32)\n",
       "  ),\n",
       "  Iext=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.3, dtype=float32)\n",
       "  ),\n",
       "  rNMDA=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.25, dtype=float32)\n",
       "  ),\n",
       "  VT=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0., dtype=float32)\n",
       "  ),\n",
       "  d_V=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.57, dtype=float32)\n",
       "  ),\n",
       "  ZT=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0., dtype=float32)\n",
       "  ),\n",
       "  d_Z=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(0.7, dtype=float32)\n",
       "  ),\n",
       "  QV_max=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  ),\n",
       "  QZ_max=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  ),\n",
       "  t_scale=Const(\n",
       "    fit=False,\n",
       "    t=IdentityT(),\n",
       "    reg=None,\n",
       "    val=Array(1., dtype=float32)\n",
       "  ),\n",
       "  init_V=Constant(value=0.0),\n",
       "  init_W=Constant(value=0.0),\n",
       "  init_Z=Constant(value=0.0),\n",
       "  method=exp_euler\n",
       ")"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node = brainmass.LarterBreakspearStep(in_size=1, d_V=0.57)\n",
    "node"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48cf8c47",
   "metadata": {},
   "source": [
    "## Run a simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "836a02cd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T08:13:07.140440Z",
     "iopub.status.busy": "2026-06-19T08:13:07.140188Z",
     "iopub.status.idle": "2026-06-19T08:13:07.379567Z",
     "shell.execute_reply": "2026-06-19T08:13:07.378720Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 1)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim = brainmass.Simulator(node, dt=0.1 * u.ms)\n",
    "res = sim.run(500. * u.ms, monitors=['V', 'W'], transient=100. * u.ms)\n",
    "res['V'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c4f59a1",
   "metadata": {},
   "source": [
    "## Visualize\n",
    "\n",
    "The mean potential `V` oscillates; the `V`-`W` phase portrait shows the conductance-based limit cycle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "011b91ff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T08:13:07.382022Z",
     "iopub.status.busy": "2026-06-19T08:13:07.381768Z",
     "iopub.status.idle": "2026-06-19T08:13:07.551661Z",
     "shell.execute_reply": "2026-06-19T08:13:07.550653Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "brainmass.viz.plot_timeseries(res['V'], ts=res['ts'], ax=axes[0])\n",
    "axes[0].set_title('Larter-Breakspear mean potential V')\n",
    "brainmass.viz.plot_phase_portrait(res['V'], res['W'], ax=axes[1])\n",
    "axes[1].set_xlabel('V'); axes[1].set_ylabel('W')\n",
    "axes[1].set_title('Limit cycle (d_V = 0.57)')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2165b08e",
   "metadata": {},
   "source": [
    "## Try it: vary the threshold variance `d_V`\n",
    "\n",
    "The regime boundaries are sharp. `d_V = 0.65` (default) gives a fixed point; `d_V = 0.57` gives a limit cycle. We report the steady-state standard deviation of `V` as a simple oscillation detector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f296b5e6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T08:13:07.554489Z",
     "iopub.status.busy": "2026-06-19T08:13:07.554204Z",
     "iopub.status.idle": "2026-06-19T08:13:08.136652Z",
     "shell.execute_reply": "2026-06-19T08:13:08.135794Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d_V = 0.50  ->  std(V) = 2.363e-06  (fixed point)\n",
      "d_V = 0.57  ->  std(V) = 1.110e-01  (oscillatory)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d_V = 0.65  ->  std(V) = 1.307e-01  (oscillatory)\n"
     ]
    }
   ],
   "source": [
    "for d_V in [0.50, 0.57, 0.65]:\n",
    "    m = brainmass.LarterBreakspearStep(in_size=1, d_V=d_V)\n",
    "    r = brainmass.Simulator(m, dt=0.1 * u.ms).run(\n",
    "        500. * u.ms, monitors=['V'], transient=200. * u.ms)\n",
    "    std = float(np.std(u.get_magnitude(r['V'])))\n",
    "    regime = 'oscillatory' if std > 1e-3 else 'fixed point'\n",
    "    print(f'd_V = {d_V:.2f}  ->  std(V) = {std:.3e}  ({regime})')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}