Whether chaos can be achieved in piecewise linear boundary value problems

Differential Equations and Dynamical Systems - Tập 18 - Trang 1-9 - 2010
E. Yu. Romanenko1, A. N. Sharkovsky1
1Institute of Mathematics, National Academy of Science of Ukraine, Kiev, Ukraine

Tóm tắt

We show that chaos in piecewise linear partial differential equations with linear boundary conditions is realizable: even the simplest boundary value problems of this kind can possess chaotic solutions in an open region of the parameter space.

Tài liệu tham khảo

Sharkovsky A. N., Difference equations and boundary value problems, in: New Progress in Difference Equations, Proc. ICDEA’2001, Taylor & Francis, London, 3–22, (2004) Sharkovsky A. N., Maistrenko Yu. L. and Romanenko E. Yu., Difference equations and their applications, Ser. Math. and its Appl., Dordrecht: Kluwer Acad. Publ., 250, (1993) Romanenko E. Yu. and Sharkovsky A. N., From boundary value problems to difference equations: A method of investigation of chaotic vibrations, Intern. J. Bifurcation and Chaos, 9(7), 1285–1306, (1999) Sharkovsky A. N. and Romanenko E. Yu., Difference equations and dynamical systems generated by certain classes of boundary value problems, Proceedings of Steklov Institute of Mathematics, Moscow, 244, 264–279, (2004) Sharkovsky A. N. and Romanenko E. Yu., Turbulence: Ideal, Encyclopedia of Nonlinear Science (ed. Alwyn Scott), New York and London: Routledge, 955–957, (2005) Sharkovsky A. N., Ideal turbulence, Nonlinear Dynamics, 44, 15–27, (2006) Romanenko E. Yu. and Sharkovsky A. N., Dynamics of solutions for simplest nonlinear boundary value problems, Ukrain. Math. J., 51(6), 820–826, (1999) Romanenko E. Yu., Randomness in deterministic difference equations, J. Difference Equations and Appl., 16(2–3), 243–268, (2010)