Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling

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单振子

Mackey-Glass system

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module FHN
    implicit none
    real,parameter :: h=0.02D0,PI=3.1415926D0
    integer,parameter :: N=500,MaxT=100000
    integer,allocatable :: neighbour_matrix(:,:)
    real :: u(N),v(N)
contains

    subroutine u0_v0()
        implicit none
        integer :: k
        do k=1,N,1
            call random_number(u(k))
            call random_number(v(k))
            write(10,*) u(k),v(k)
        end do
    end subroutine u0_v0

    subroutine fnf(p,sigma)
        implicit none
        integer :: k,i,j,t,p,count_number(N) !count_number 环数
        real :: func_u(N),func_v(N),epsilon=0.05D0,gamma=0.7D0,beta=0.0001D0,sigma,a(N),effect_u,effect_v,&
                &b_uu,b_uv,b_vu,b_vv,t_up(N),t_down(N),t_each(N),omega(N)
        a=0.5
        count_number=0
        t_up=0.0
        t_down=0.0
        t_each=0.0
        omega=0.0
        b_uu=cos(PI/2.0-0.1)
        b_uv=sin(PI/2.0-0.1)
        b_vu=-b_uv
        b_vv=b_uu
        do t=1,MaxT,1
            do k=1,N,1
                effect_u=0.0D0
                effect_v=0.0D0
                do j=1,N,1
                    effect_u=effect_u+neighbour_matrix(k,j)*(b_uu*(u(j)-u(k))+b_uv*(v(j)-v(k)))
                    effect_v=effect_v+neighbour_matrix(k,j)*(b_vu*(u(j)-u(k))+b_vv*(v(j)-v(k)))
                end do
                func_u(k)=u(k)+h*((u(k)-(u(k)**3)/3.0-v(k)+sigma/(2.0*p)*effect_u)/epsilon)
                func_v(k)=v(k)+h*(u(k)+a(k)+sigma/(2.0*p)*effect_v)
                if(t==MaxT) then
                    write(20,*) k,u(k)
                end if
                if(t>50000) then
                    if(k==500) then
                        write(40,*) u(k),v(k)
                    end if
                    if(v(k)>0.5.and.func_v(k)<0.5) then
                        count_number(k)=count_number(k)+1
                        if(count_number(k)>1) then
                            t_each(k)=t_each(k)+t*h-t_down(K)
                        end if
                        t_down(k)=t*h
                    end if
                end if
            end do
            u=func_u
            v=func_v
            if(t==MaxT) then
                do i=1,N,1
                    omega(i)=2.0*PI*((count_number(i)-1)/t_each(i))
                    write(50,*) i,omega(i)
                    write(*,*) i,t_each(i),omega(i),count_number(i)
                    write(60,*) u(i),v(i)
                end do
            end if
        end do
        return
    end subroutine fnf


    !建立网状结构
    subroutine neighbour(K)
        implicit none
        integer :: K !单节点K个邻居
        integer :: i,j,number
        allocate(neighbour_matrix(N,N))
        !初始化网络矩阵
        neighbour_matrix=0
        do i=1,N-1,1
            do j=i+1,N,1
                if(abs(i-j)<=K/2.or.abs(i-j)>=N-K/2) then
                    neighbour_matrix(i,j)=1
                    neighbour_matrix(j,i)=1
                end if
            end do
        end do
        return
    end subroutine neighbour

end module FHN



program main
    use FHN
    implicit none
    integer :: p
    real :: sigma,r
    open(10,file="data_u0_v0.txt")
    open(20,file="data_k_u.txt")
    open(30,file="data_ak.txt")
    open(40,file="data_t_u.txt")
    open(50,file="data_k_omega.txt")
    open(60,file="data.txt")
    call random_seed()
    call u0_v0()
    write(*,*) "请输入耦合半径r和耦合强度σ："
    read(*,*) r,sigma
    p=nint(r*N)
    write(*,*) p,sigma,r
    call neighbour(2*p)
    call fnf(p,sigma)
    deallocate(neighbour_matrix)
    close(10)
    close(20)
    close(30)
    close(40)
    close(50)
    close(60)
end program main