MATHEMATICAL PUBLICATIONS

Citations:

• Applied Mathematics Letters, 7(5):57-60, 1994.

Abstract: This paper gives two lemmas dealing with the continuity of solutions of ordinary differential equations with respect to perturbations in the vector field and initial conditions when the equations contain a linear part. The basic lemmas in ODE theory are special cases of these lemmas. The lemmas are useful in easily deriving some nonlinear ODE stability results. They are also useful in certain singular perturbation problems.

Notes:

Citations:

• Proc. IEEE Workshop Physics and Computation, Dallas, pp. 265-274, Nov. 1994.

Abstract: We demonstrate simple, low-dimensional systems of ODEs that can simulate arbitrary finite automata, push-down automata, and Turing machines. We conclude that there are systems of ODEs in $\R^3$ with continuous vector fields possessing the power of universal computation. Further, such computations can be made robust to small errors in coding of the input or measurement of the output. As such, they represent physically realizable computation.

We make precise what we mean by ``simulation'' of digital machines by continuous dynamical systems. We also discuss elements that a more comprehensive ODE-based model of analog computation should contain. The ``axioms'' of such a model are based on considerations from physics.

Notes:

• The simulation results of my paper Universal Computation and Other Capabilities of Continuous and Hybrid Systems, interpreted in a physics light. Plus a start towards a model for analog computation with ODEs.