The book by Gleick is a classic early popularization. The others are good introductions to the topic.

- Handbook of Applications of Chaos Theory byCall Number: 2nd Floor QA320 .H35 2016ISBN: 9781466590434Publication Date: 2016-06-01
- Nonlinear Dynamics and Chaos byCall Number: 2nd Floor Q172.5.C45 S77 2015ISBN: 9780813349107Publication Date: 2015-03-01
- Introduction to Modern Dynamics byCall Number: 2nd Floor QC133 .N65 2015ISBN: 9780199657032Publication Date: 2015-01-01
- Nonlinearity, Chaos, and Complexity: the dynamics of natural and social systems byCall Number: Q172.5.C45 B477 2005Publication Date: 2005
- Galloping Instability to Chaos of Cables byCall Number: 2nd Floor TA654 .L88 2017ISBN: 9789811052415Publication Date: 2018-01-26
- The Nonlinear Universe: chaos, emergence, life byCall Number: Q172.5 .C45 S36 2007Publication Date: 2007

The expression “dynamical systems” in the literature refers often to both real systems (physical, chemical, biological, etc.) that follow a well-defined evolution in time (a trajectory) and also to the systems of differential equations that are used to model them. Complexity studies are often led to consider dynamical systems that are **nonlinear**, **chaotic** or sometimes **indeterministi**c.

Linear systems are described by equations that comply with the principle of linear superposition: if X1 and X2 are both solutions of an equation, then X1 + X2 is also a solution of that equation. If this is not the case the equations (or the system they represent) are said to be **nonlinear**. If a linear equation represents the functional dependency of a variable x on another variable y, in general if x is increased by a constant factor the variable y is also increased by a proportional amount. Linear equations are relatively easy to solve and analyze, while nonlinear equations are usually difficult and often impossible to solve.

A dynamical system is **deterministic** if given the exact mathematical description of its state at one time there is only one possible future trajectory. If the system is placed again in the same state the same sequence of states will be exactly repeated.

**Chaotic** systems are deterministic systems that, paradoxically, are highly unpredictable. This unpredictability is a consequence of an extreme sensitivity to initial conditions found in some nonlinear dynamical systems. The smallest variation in the quantities that specify the state of the system at one given time leads to rapidly divergent trajectories in its future evolution. Since the determination of the initial conditions is always limited by a non-eliminable degree of error, chaotic systems become immediately uncontrollable and unpredictable.

Articles on dynamical systems and chaos theory are found in specialized journals and in mathematics and physics journals dealing with nonlinear systems. Among them the following are available at Linda Hall:

- International journal of bifurcation and chaos in applied sciences and engineeringCall Number: LHL SerialsPublication Date: LHL owns 1993 to 2009
- Discrete dynamics in nature and societyCall Number: electronic resourceThis online journal is available from within the library.
- Nonlinear DynamicsMany issues from 2001 to 2005 available at LHL.