A giant iguana isn’t something we’ve come to expect as a key component in an L.A. novel, but that’s what local writer Diana Wagman has done with “The Care and Feeding of Exotic Pets.”

A brisk and vividly drawn kidnapping tale, Wagman’s fourth novel hinges on the 7-foot-long lizard of its title, but its core lies somewhere far more familiar to those who call Los Angeles home.

At the center of Wagman’s story is Winnie Parker, a 38-year-old single mother who split from her wealthy game show host husband some years ago. During a morning of wrestling with the moods of her 16-year-old daughter and the sorts of mundane errands that generally consume adult life, Parker is abducted by Oren, the roommate and caretaker of the exotic pet in question (known as Cookie to his friends).

Though at its root a hostage thriller – and a pretty tense one at that – the power of Wagman’s book lies in the details. Winnie’s kidnapping comes early, with an unsettling banality that’s too easy to imagine for anyone who has been too caught up in their day-to-day to be careful, and Wagman does a terrific job in tracking Winnie’s shift from confusion to terror as she understands the gravity of her situation. The tension moves closer to a boil as she’s pulled into Oren’s overheated Altadena house, which is kept at a sauna-like temperature in deference to Cookie’s needs.

At first, the iguana seems to be what drives Oren’s crime – a black-market reptile trade is introduced – but as the book shifts into Oren’s twisted point of view, she reveals that his motivation is even more unsettling. An abused child of carnies, Oren’s back story is a bit over the top, but Wagman captures his disturbed state with a variety of on-a-dime mood swings and a habitual desire to ask “Why me?” while deflecting any blame for his actions as he slowly unravels.

Winnie is one of the biggest contributors to that unraveling as she shrewdly works every possibility for escape, acting just as any other wild animal in captivity might. The anonymous sprawl of L.A. becomes a player as she and her captor take a pivotal trip across town, ducking traffic to navigate through the warehouses near downtown as Winnie futilely tries to draw attention from her fellow drivers.

As much as that chilling urban invisibility rings true – ask yourself how often you’ve really looked inside the car next to you – the idea gets stretched too far in an overlong public fight scene between Winnie, Oren and a reptile smuggler, who may be even more disturbed than Winnie’s kidnapper. Still, the occasional false note is easy to overlook given the overall depth of Wagman’s narration as she follows characters around Winnie’s orbit.

First is Winnie’s wealthy but dimly insecure ex, Jonathan, who is midway through a uniquely Hollywood sort of midlife crisis. Alternately regretting and celebrating his decision to take up with a young yoga instructor, he affectionately lingers at the Echo Park home that he and Winnie once shared just as her captivity is beginning. He later drifts into a tearful panic attack at his own mortality, shortly after learning that his successful game show gig isn’t as temporary as he’d hoped. “Sorry,” his agent says while breaking the news about another disappointing audition, “You’re just so damn recognizable – as yourself.”

Another key figure, Winnie’s daughter Lacy, is a pleasure to follow as she begins coming of age. She at first appears as a fairly typical teen trying on different identities, one of which has chillingly unexpected consequences. While Winnie struggles for her survival, her daughter is coming alive as a romance with a childhood friend develops. Wagman frames the flirtation in lovingly intimate details, such as the awkward dance of eye contact as a crush becomes something more.

But “The Care and Feeding of Exotic Pets” tilts on Winnie’s strength. In her, Wagman has constructed a magnetic figure who is easy to root for whether she is fighting to escape or bitterly recalling her ex-husband’s honeymoon, wondering, “Was there really a place called Bora Bora, or was it just a euphemism for ecstatic sex?” The book also benefits from breathless pace and a dialogue-heavy structure that hints at Wagman’s screenwriting experience and keeps the pages turning.

Of course, to paraphrase Chekhov, if you introduce a big iguana in Act 1, it had better go off at some point, and Cookie is a pivotal player in Winnie’s struggle. As is Los Angeles — whether reflected in the raw-nerved struggles of a famous ex or Winnie’s wreck of an ex-actress mother, the city and its proximity to celebrity remain within frame.

“Every idiot with a cat on YouTube is famous,” Oren spits when Winnie attempts to bargain for her release with a promise of a shot at fame.

Eventually that same promise gets turned back toward Winnie, and while doors may open for people (and their pets) to escape from captivity, ultimately they can only be who they are. And sometimes that’s enough.