#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Feb 15 11:34:37 2021
author: Xiaoting Yang
"""
import numpy as np
import matplotlib.pyplot as plt

plotdir='./Figures/';

    
# set parameters for the delayed oscillator
DT=0.1 # time is in month
alpha=0.54# 0.75: standard value; 0.54: growing oscillations; 0.51: decaying (without 2nd mode Rossby wave)
delta=round(8/DT) # for 1st mode Rossby wave

# set initial conditions:
i_start=round(delta)
i_end=round(1200/DT);

Nh=i_end;

# start at fixed point plus a small perturbation
h=np.zeros((Nh,1));
h[:i_start]=np.sqrt(1-alpha)+0.001;

for ii in range(i_start,Nh):
    h[ii]=h[ii-1]+DT*(h[ii-1]-alpha*h[ii-delta]-h[ii-1]**3);

# make figure
# define time axis
Time=np.linspace(0,1,Nh)*i_end*DT/12

plt.figure(figsize=(10,10)); plt.clf();
plt.subplot(2,1,1)
plt.plot(Time[i_start:],h[i_start:],color='b',linewidth=1.2)
plt.xlabel('Time (year)'); plt.ylabel('h');
plt.title('Time series'); plt.xlim(Time[i_start],Time[-1])

plt.subplot(2,1,2)
plt.plot(h[(i_start-delta):(-delta)],h[i_start:],color='r',linewidth=1.2)
plt.xlabel('h(t)'); plt.ylabel('h(t-year)');
plt.title('Constructed phase space')

plt.tight_layout()
plt.show()
#plt.savefig(plotdir+'delayed_oscillator_alpha'+str(alpha)+'_'+tail+'.png')