Chaotic Real-Valued Sequences By Skew Tent Map

0. Note

1. Introduction

2. Tent Map

3. Chaotic Sequence

3.1 For “x” equals to 0 and 1, and “c” equals to 0.5

3.2 For “c” equals to 0.6 and x = 0.3 and 0.8

3.3 Sensitivity to Initial Value

3.4 Distributions of the sequences

4. Conclusion

5. Source Code

function t = stcsfp(xo,c,N)% === TENT MAP === %X = 0:.1:1;for n = 1:11
if X(n) >= 0 && X(n) < c
T(n) = X(n)/c;
elseif X(n) >= c && X(n) <=1
T(n) = (1-X(n))/(1-c);
else
printf("x initial must be from 0 to 1");
end
end
% === MAIN CALCULATION === %
x(1) = xo;
for n = 1:N
if x(n) >= 0 && x(n) < c
t(n) = x(n)/c;
x(n+1) = t(n);
elseif x(n) >= c && x(n) <=1
t(n) = (1-x(n))/(1-c);
x(n+1) = t(n);
else
printf("x initial must be from 0 to 1");
end
end
%Plot Tent Map%
figure
plot(X, T, xo, t(1));
title("Tent Map");
xlabel("X");
ylabel("T");
%legend("fill this in")
%Plot Sequence%
figure
plot(t);
title("Sequence Generated");
xlabel("n");
ylabel("t(n) or x(n+1)");
ylim([-0.1 1.1]);
%legend(["fill this in"]);
%xlim([1 20])
%Plot Histogram%
figure
hist(t, 0:.01:1);
title("Distribution");
xlabel("Value");
ylabel("Count");
xlim([-0.1 1.1]);

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