Quadratic non-stochastic operators: examples of splitted chaos

There is one-to-one correspondence between quadratic operators (mapping $${\mathbb {R}}^m$$ to itself) and cubic matrices. It known that any operator corresponding a stochastic (in fixed sense) matrix preserves the standard simplex. In this paper we find conditions on (non-stochastic) ensuring Moreover, construct several non-stochastic which generate chaotic dynamical systems These behaviors are splitted meaning simplex partitioned into uncountably many invariant (with respect operator) subsets restriction of system each set chaos in sense Devaney.