Can anyone suggest some examples for bifurcations and chaos without delay? I want to know whether we frame an equation or system of equations with chaos without delay. Can anybody help with some examples which exhibit chaos or bifurcation? Can you also give any particular examples of which influences cause the system to become chaotic?
J. C. Sprott proposed some systems without equilibrium in which he showed the bifurcation and lyapunov exponent. Most literature will not show the bifurcation of systems greater than 3d.
Not sure if i understand the question fully, however delayed differential equations are part of deterministic systems, explicitly dependent of the dynamics of such systems which accounts on past states. These systems come with an uncertainty on the initial state. May be Lorentz chaotic or ergodic theory can be an example. Sorry I have moved on from this topic for a while, but this is what i could think of.
There are a lot of dynamical systems without delay which exhibit chaos and bifurcations. See for example the attached file about an interesting 2D discrete system: the Tinkerbell map.
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