Even more results on catchup

As highlighted in script below three coupling parameters epsa,epsi,epss are used in loglevel description. z_k is log y_k, v_k is same as y_k in coupled system (just notation). The phase lag induced by ta*Exp[-eps(t-ta)] will decline exponentially, the faster the larger coupling eps.

New script for generating multiple initial conditions:
(*Parameters for standard model*)
b = 1;
c=0.6;
alpha = 0.015;
lambda = 1.5;

La0 = 0.8;

ya0= b/La0
yi0=1.25
ys0= b*c/((1-c)(1-b/ya0)) (* initial condition for Yi(0) = 0 *)

Ls[b_,c_,ya_,yi_,ys_]:=(1.0 +b*(1/yi-1/ya))*c/(c+(1-c)*ys/yi)
La[b_,c_,ya_,yi_,ys_]:=b/ya
Li[b_,c_,ya_,yi_,ys_]:=((1-c)*ys*(1-b/ya)-b*c)/(c*yi+(1-c)*ys)

yi0=1.25; (*yi0=ya0=1.25*)

tmax=700; (*time range*)
Lmax = 1.0; (*employment range*)

(* let leader start tau ahead *)

deltaT =50;
Kmax=5;
tau=Table[(k-1)*deltaT,{ k,1,Kmax}]

(*Parameters for coupled model*)
epsilon = 0.005;

(* phase different eps: use loglevel-coupling *)

epsa=5.0*epsilon;
epsi=5.0*epsilon;
epss=1.0*epsilon;

betaa=lambda*alpha;
betai=lambda*alpha;
betas=alpha;

z[t_,ta_,beta_,eps_]:=beta*(t-ta*Exp[-eps*(t-ta)]);
v[t_,ta_,beta_,eps_,y0_]:=y0*Exp[z[t,ta,beta,eps]];

k=1;
Plot[ { usw. usw

Four simulations showing employment in all sectors

Regard indirect impact on service sector. Is so rapid dropping employment in industry expected for followers?

1a) strongly coupled industry
epsa = 1.0*epsilon
epsi = 2.0*epsilon
epss = 1.0*epsilon

1b) strongly coupled agriculture and industry
epsa = 2.0*epsilon
epsi = 2.0*epsilon
epss = 1.0*epsilon

2a) very strongly coupled industry
epsa = 1.0*epsilon
epsi = 5.0*epsilon
epss = 1.0*epsilon

2b) very strongly coupled agriculture and industry
epsa = 5.0*epsilon
epsi = 5.0*epsilon
epss = 1.0*epsilon